Chapter 1. Measuring Spread: the Standard Deviation

true
Stat Tutor
true
true

Questions 1-2

0:36

Question 1.1

VPFZe16eDfXrvb/kBzIVCQVBgL1LrC1jrCUIlj3iZTzzvPU4fYx1zLsswdyu8YBEWUthRy7qG4YZv5XylIjfQNSjgQJb3LJiokFM1N2ioYOe2KYt4235734NCxIU+i/bEBXLgA==
Correct. Both histograms are centered at the same place.
Incorrect. Both histograms are centered at the same place.
2
Try again.

Question 1.2

71Tz/vsQx/RSup9oMsGmHWv3vDCnAU2vt+cpznVJTez+FfTIqQBCPmjsPrK/8IvvmIhO2kzBE2aEiL9HCSjZeFQVIrYrTmCdILpxqJk+ND6SmBM8+7uZywCjmAvEaV0/C4QZCg==
Correct. The histogram for Atlanta temperatures is much wider than the histogram for San Diego temperatures.
Incorrect. The histogram for Atlanta temperatures is much wider than the histogram for San Diego temperatures.
2
Try again.

Questions 3-4

1:06

Question 1.3

VPFZe16eDfXrvb/kBzIVCQVBgL1LrC1jrCUIlj3iZTzzvPU4fYx1zLsswdyu8YBEWUthRy7qG4YZv5XylIjfQNSjgQJb3LJiokFM1N2ioYOe2KYt4235734NCxIU+i/bEBXLgA==
Correct. The histograms are both centered at the same place.
Incorrect. The histograms are both centered at the same place.
2
Try again.

Question 1.4

71Tz/vsQx/RSup9oMsGmHWv3vDCnAU2vt+cpznVJTez+FfTIqQBCPmjsPrK/8IvvmIhO2kzBE2aEiL9HCSjZeFQVIrYrTmCdILpxqJk+ND6SmBM8+7uZywCjmAvEaV0/C4QZCg==
Correct. The histogram for SWBDX percent return is narrower than the histogram for SWLBX percent return.
Incorrect. The histogram for SWBDX percent return is narrower than the histogram for SWLBX percent return.
2
Try again.

Questions 5-6

3:03

Question 1.5

OQZnlvptm0YOpjHlU4S56/H5/lPTMhsy25VTMyH9InRMl0Hgv0eyMyhzxOPVbX0dVRpWV3sVKLLarwqc2TrnzBmlk7XM3Dm0Z1EJTMcwJMGauK5QBYRrmZdJeOXXSSMjVI2jgD90HOaK2q2wJJwtKXG0j9fiyZTqymgIE/TkPjli2aYUa3nvdOwwo0pg7en/4g/jiBREhWErA2jPauUO1Twf9j2iItiim1QSMIsJlKYzUoQQfHJcMUyeJYy29fxwioCAOlQRtGARh0QRmMyjpiVzPBoWoSaf7jhp56JhKcc=
Correct. A deviation is equivalent to the distance a value is from the mean. So, a deviation is the difference between the observation value and the mean, \( \overline{x} \).
Incorrect. A deviation is equivalent to the distance a value is from the mean. So, a deviation is the difference between the observation value and the mean, \( \overline{x} \).
2
Try again.

Question 1.6

15dfMlY8NwiTATi3IUM3aCPAYX2r71MeUzgpUe9CGA4HanCJ9i4JETikDYvD3ancAyqeSzpJV+8Jw4E1LWYeSLxvD4p1obsYU/a/YyHwNAMl3BZrsFeJJfTpGRtK5rElufyPM9wnQERWS44JsWY7sk/z09V5lMRd3LVvlYY8H+zUKvJae9L3jp4SOf2a6cSssLvNVdo3Zo8KnBHvDiSpG+11NucF8ymjZnuKdCQxkKbef1zT0KcVZo7xDb0wuejDseFSdw/czjggOnhU8WN2bVe/vsulEen0fxJLmea3D5DW9f0GoKr7nNRYGBYKuyQUGfxzRqaX5Z4=
Correct. Since the observations below the mean have negative deviations and the observations above the mean have positive deviations and the mean is the balance point, the sum of these deviations is always zero.
Incorrect. Since the observations below the mean have negative deviations and the observations above the mean have positive deviations and the mean is the balance point, the sum of these deviations is always zero.
2
Try again.

Question 7

4:01

Question 1.7

jmg6j+X9n6Galqb3yg46XxbugVJLQHPUdRU/24GZvgzSS/HCYYx/GUNPjf6QIy2be26eyDY9WTcFeyuw/ZlrYCXza6WZu7dAeGHUuo4I5ygbjZCSU/m7HIE/z3Q2pv5l
Correct. “s” is the symbol for sample standard deviation.
Incorrect. “s” is the symbol for sample standard deviation.
2
Try again.

Questions 8-9

6:08

Question 1.8

Tp5GafbY7aVeo2jrisp1NncxwztKN50uiEq3WD/rK9SLnsjxFVH3ezTNWmwfyjn/h/sXxIBWX6XmneGMrO1u4NtAXRVoMDocUbsUfTnAsU/1UZDay8yeVJbhPKox28oOIGdAw7GBUFdzKA1IxpvzlsEpHLf+ZzH/d+mx4XFQteFI2lyqIgV2VdxJ05c5VSwLXLY5YRAphNPbErlD6pxx7Ip9ZUdSC0z4MdXoaro14f3nCoCcgQagAsAZRVJhxf3JtGnz/A==
Correct. Variance is the average of the squared deviations. Since a squared deviation is graphically represented by an area, variance is the area of the average squared deviation.
Incorrect.Variance is the average of the squared deviations. Since a squared deviation is graphically represented by an area, variance is the area of the average squared deviation.
2
Try again.

Question 1.9

6IKqvZVRUtX3I6kfp8L58d55Po/KKwo/u4vWxTq4nU+c1ebb+sO7s0sFQEcVMguAJUHk4JtG0lXIF0C+JbhTNnZko+VAwX7nFHlEy9GZsa3SzCuJmvCSrvxMijnhuL1xO/5lbzxejB673TN55x02jFGrv/JTdVNbl1wtK9mVrtuMJ7XZjBasyMZxw9lV9qCeWg7yC1NZA2TBwQioVwvw0pA7L9h2d3b0x+Ct0FZnOA+m68IosgPehGYfdP4wTVm4yTnV6QhAhAL3xKvRasx8uLZ+37A=
Correct. It would be nice to either delete the negative signs or to take absolute values, but mathematically, this is too messy. Using squared the deviations has nice mathematical properties.
Incorrect. It would be nice to either delete the negative signs or to take absolute values, but mathematically, this is too messy. Using squared the deviations has nice mathematical properties.
2
Try again.

Questions 10-11

6:27

Question 1.10

GjlgzdVm8tzP80Kp2IK8h/9+VUKY3/RFEa5XqBkNx9Sled0KeSp6yjT6rSHlHH6QkCX1LOcqZXpgCWqdEuHEVbT9JjZRO+FNwIcpO38QPDw2KbPURcnf2bfibZQeAxeFE22tgw==
Correct. This is a correct statement.
Incorrect. This is a correct statement.
2
Try again.

Question 1.11

SN8YqzD6RO8GMm2NVlfdE4mKT6NzsrDljlDwE5IlFxZr887+dSBmuKdhgE/D1H9+JVuEEwKZJGHyzbhBEKIlQAgnNGawxzROuPvjyQT8ydLjVtSsZ2tRLa3L4phg8xgnQ0Ss/Si+kCMBG0pO2/n1Mtj8QXrsOfadmsyR57YPTdtsOPfQYOIrWsYxLQ7Rj4amx0RZ9mfZgX2mvp8Oah9ICSgh9KoKvHN0P7UtBNLToDWERXWS+hNHWYu9Cp8QOvMTJZFhJMBYsprQNtlGJ+mEKQxL3Pk65BQp4NErz0KNuFG38AAPM9zA0PuIl+4+pFrh
Correct. Since variance is the average of the squared deviations and we find standard deviation by taking its square root, standard deviation is the length of one side of the average squared deviation.
Incorrect. Since variance is the average of the squared deviations and we find standard deviation by taking its square root, standard deviation is the length of one side of the average squared deviation.
2
Try again.

Question 12

9:04

Question 1.12

ewzbiqyxapfq6s3hS2rFaQEoIWrlbCQ686tIqi+2t6SYd+EgKaSJhgRGj6+FzPuk615CJriKJRWblWaPuz1p7RdfKK8RitGY7EDmKtnq62b5q9bi5QFYnNZLObUyKIESdVQJZxg9bn5clesA
Correct. No one likes to spend time computing standard deviation by hand.
Incorrect. No one likes to spend time computing standard deviation by hand.
2
Try again.

Applet

9:19

Questions 13-17

10:12

Question 1.13

A0Nw2EBbZIPgt2LYBpHQU0CS4EvQXjlau147lKYJSghxjD3yRxD+YuVr8xg+rDl/4lPqcw==
Correct. We always take the positive square root of variance when we compute standard deviation. Standard deviation is zero when all of the observations have the same value.
Incorrect. We always take the positive square root of variance when we compute standard deviation. Standard deviation is zero when all of the observations have the same value.
2
Try again.

Question 1.14

woJARVP0KMHP/LQxD4pqT7edqKUNF+bz1gGbJkyRardl0obW0sFmPeIAjN3epuqgJRMKEUwWjIIyF22HmbZUWA86VOWhg03EjBFgyGsLgz22hrdH47ekyaeA3BTu8BROUC/pjZ4NUQ5NkXSpHtZEOpT6mUI0UUdKFsTH6qUw1QXDYH9K9x/N+8UcdKhAcI9GLtuOSa9YHGv7mjOy0iXECu8FCG7uecfV7+bSOXu1ZiYg1f8VQpKIS/lEwZ4=
Correct. Standard deviation measures variability. This is very important to know.
Incorrect. Standard deviation measures variability. This is very important to know.
2
Try again.

Question 1.15

PyE94QJgpSLLP6wrqwETqXVaMpRjVeA+/L9enG5FJHTOlATEv7JjPl1PHSobW4I71lGtpBL6gYfuuxLcjLYEhe4GI8UMeH/IgjKQ635Q/YHftA77MZ9AVu3V3GS27Yn8TH81nYX2yfbT6Cyqu2+F8u/x0vIQJOr8ob7JpEZ5UE39qCykb9df2nJzcLhdhlH1S0VzBxAjQzEyprOaddsBeQeJ10JcE9V58RaOBBuD6++2RIAzyjLv5L1M86AF1Qo4BMsPeK9jNWAdmmjhcu24wabyb6SbvuMR7MKvtveNUSKEZ+V8hNGVt3+pFtkvSHTirPnFjoMsqc0OanbAaw7O2WuayDyNeaa9zBsGoKeW7WG02c5K
Correct. When all of the values in a data set are the same, their standard deviation is zero.
Incorrect. When all of the values in a data set are the same, their standard deviation is zero.
2
Try again.

Question 1.16

Z9ArQSkbX4xmTUH21wEGjmTM7NiSXg3umrQ/SVlt038lmHZYj3TWdMr1Cz0jO7GWmJ9dbiIyHH5H8DuuxiIsteyUoCBQ7wHaWaWu3cURP97bG2uQmDR/ZsiwvMgnhUBn0AoWwGcnp3ZJa4FO8PzXojJIo9wdlhOVWi7LCvjmIdsk6/m7k6IP3ixcrbsaCyeExFOiNfeX5Fw9DjiaOO2olrDJIc6uTpPjVmej2sKnNLcN3kDTsG9/ktx1zq0zX4CjBhT8x9xOF9zs5e90kSB8+ZS62M8=
Correct. ‘26’ is an outlier and will inflate standard deviation as it adds more variability. The more the data vary from the mean, the greater the standard deviation.
Incorrect. ‘26’ is an outlier and will inflate standard deviation as it adds more variability. The more the data vary from the mean, the greater the standard deviation.
2
Try again.

Question 1.17

N0v7/xYmV7glZAonhdQ+Q/iYgj4v+Qkx+1qMENycWoafs+Zd5enHCR0xeveBBjs87lvhXh1ua7cEFo+nk5SRfWKpzY2DaQckWtZ1oWn/CNSpCsPAIE+NJOhxrhE7iTT1OR7Xl8dFl0u1M/SMhP9Xl5tkExZYQiwQDtc4OShphgwYf/vR3yHKRcRj5dYyA3NrMnP42LXBCJF9ckg8CKaVPg==
Correct. Standard deviation has the same unit of measure as the data.
Incorrect. Standard deviation has the same unit of measure as the data.
2
Try again.

Question 18

11:28

Question 1.18

qeYki1cmcgaoerrSUN8PkpFonTwvgT+prvbpdfiT+Kgz/4S+Y9bbAbpgGtDja7qLfj7dNAvqfyKEWOuurseYjVfhBSE4KBGtjvghWl//ybmeBxQsW4c+COTGTdJUV/lADpmnThCug20VIpRF
Correct. We divide by “n – 1” when computing sample standard deviation for mathematical reasons.
Incorrect. We divide by “n – 1” when computing sample standard deviation for mathematical reasons.
2
Try again.

Question 19

12:04

Question 1.19

51OGSM93ambWV91ni2fwSzqE6zniD1mI80WyhiCfwNm1OzJgSv03nVF3W2x8+dip8nPGCiOTYF2DmpU0pdSaeT0q+E8ucJIoi4lIsmoc00AhRDavnr5x9CUWm6TNvon3ect+CZL8rayZGVhePRSK3UumhyPqxdTyb/g4kBt9rcmpPFCxP2n8jvueij4UOfY8RidJCNpN66Ct3thmIOQaw/+Uq8dGb1hMRmZWm9lTfq45S5rNgLK6wFdaZG2TpDdHHoMCl5jdQy+W3x3Ev0tNF/DRa1ZWxA5ho1K9W4v7ZccnGpdF2gRXwCvrd5V39GJsY/6NaTF7qO01specUFtKizlzg45E15syFuqklU8ctYb2Xhi4iWvAG73aoCyHm9tooTwo4g==
Correct. Since outliers affect the mean and the mean is used in computing standard deviation, standard deviation is also affected by outliers. In fact, an outlier always increases standard deviation.
Incorrect. Since outliers affect the mean and the mean is used in computing standard deviation, standard deviation is also affected by outliers. In fact, an outlier always increases standard deviation.
2
Try again.

Question 20

13:57

Question 1.20

yKaGtDyPYxflA/TvQBiiuGfjWJ1LPDcC06uzgtOe9cam6rlEXznWQWGCDhETVB2HF9FKfhwwMpAasUwGsI6FKhidPEZjItsvp8NygQv/MVEyaP0FC50xgcgX6ivlMV9lQNIf7pGg65EKFxh+o+8q2w==
Correct. range = maximum minus minimum = 47 – 34 = 13
Incorrect. range = maximum minus minimum = 47 – 34 = 13
2
Try again.

Question 21

14:17

Question 1.21

DY+gKf5TqXp4Fi86TMBDrW/S+qSEyL5DuuN29/ZF1wn2V8hvoBMbzd5/ZBK3dv55hoRQR0e40N53MQ6VshT57TyaVZeC7X4mx8zfVMUirD1EDisOSaERjNPL5epaLJgCnY3EqBlV7RPceBDR0a/Ni7jsASptY/qMY081xc94k0Tv1xpmKmk4GA==
Correct. Range = maximum minus minimum = 540 – 360 = 180 and 180/6 = 30. Note that 360 and 540 are approximations.
Incorrect. Range = maximum minus minimum = 540 – 360 = 180 and 180/6 = 30. Note that 360 and 540 are approximations.
2
Try again.

Question 22

15:14

Question 1.22

2fco55jxl1o+AefAYEqVFGbO1NGYEjLjRTz4yU2wRkNaAcWemmRr2MgbjxS1lsdgmlwZnfWJYEO0p7o579wohZM1ygPou0p/kcKeYVuxXw/v7Q/vAyUBHMtt9L1Mtu/1agxM43AJ8VYnN+g94uXMzGAaN3FthBgM17D/AMRiSzY=
Correct. Range = 5125 – 1625 = 3500 and 3500/6 = 583.33 or approximately 600 grams.
Incorrect. Range = 5125 – 1625 = 3500 and 3500/6 = 583.33 or approximately 600 grams.
2
Try again.

Question 23

16:11

Question 1.23

5eJPFuw+y8cYbMizLP5CNfgwECp1SavaMo353eskWtYHnFpioBT+AmfO2axOopqnT/MnwBZa6mINRaiU+jqg3VXOPMuuMJ03dp3litxtZbO/rxdfsPLRx96SLBsfIvCWHazbXY15Q/9ZiL+UYhHvZ7AMBRsi3vfAVQ9ywh0ykigrmGIW3GST9xPkxZEW4HS9bfIH+lECErtSsrXrMCaLFflDIUfe+WbJMUSYsOi3mEg1oJSBx60/yZHy8OcprZJVsrCCNH8xrvPkRy5K
Correct. Outliers always inflate standard deviation so the standard deviation computed with these seven extreme values will be greater than the standard deviation computed without these seven extreme values.
Incorrect. Outliers always inflate standard deviation so the standard deviation computed with these seven extreme values will be greater than the standard deviation computed without these seven extreme values.
2
Try again.

Question 24

17:17

Question 1.24

Lb/YHwxzXqW9JAn44zaRWHUGJktZGHAbgrpqt+f+cprN/sedAXFVcH7P6kayh3YGkdv/UcFYmBLOh6jvvseUPg2FS6GG0vXnE4w0mHFnF3CpkQr159+GR0WeRBH2rNJnKtq/0ZtmtJldcMGZwxb1S0zGwXqgtExjhbgfSQ==
Correct. Since the temperatures in San Diego are less variable than the temperatures in Atlanta, San Diego will give a more stable climate.
Incorrect. Since the temperatures in San Diego are less variable than the temperatures in Atlanta, San Diego will give a more stable climate.
2
Try again.

Question 25

17:54

Question 1.25

4iomhBWJo4G0QfwahetKYyDv1TN7bm5rSEFT047KL+iBbegXNMwoGWaCi/V25tXRqHUnhoKQbZLl5SzAR9ORiz8mf1uanBvswCaAgy7O5jUi/QIRYDmH+KJ0ApSTWnckQqRlbsF4wpqR+v0zE8X9Xu4qxYsZFUWfY3ahPeihxgGMSKEibBsrGbQoshhZUt4ToeDgqnQzTjJXt7Go6RkIhIHkWhjOvxReYH6RaGmDdbZH2NJPJsFgh3RXHhFK+bO7KXtQSKr4VXUNhfQD3iflywVCZYr+AUkx
Correct. The Schwab total market bond index has more variability and consequently, has a possibility of giving a greater return. It also has the possibility of giving a lower return.
Incorrect. The Schwab total market bond index has more variability and consequently, has a possibility of giving a greater return. It also has the possibility of giving a lower return.
2
Try again.