Measures of Central Tendency and Dispersion in Statistics

1. Consider the following is data on the 9-month salary of mathematics faculty members (to the nearest thousand dollars) in the year 1999-00:

61 63 72 80 70 76 97 60 57 65

67 73 66 75 61 54 61 65 70 68

53 50 50 40 51 44 62 57 51 52

50 57 52 52 56 46

Use class width = 10K. Complete the following frequency table:

Class 39.5 − 49.5 49.5 − 59.5 59.5 − 69.5 69.5 − 79.5 79.5 − 89.5 89.5 − 99.5

F req

2. Following is the grand total (out of 400) of scores obtained by students in a class.

386 343 287 394 303 280 333 389 376 350

388 380 320 391 371 354 366 354 284 298

327 386 380 370 363 382 362 384 343 352

350 391 345 385 310 380 381 362 326 82

391 328 345 376

We use class width = 50. Complete the frequency table of the date data in (1.2):

Class F requency

51 − 100

101 − 150

151 − 200

201 − 250

251 − 300

301 − 350

351 − 400

If a data value falls on the boundary, count it on the left interval.

3. The following is data on the weight (in ounces), at birth, of some babies.

74 105 124 110 119 137 96 110 120 115 140

65 135 123 129 72 121 117 96 107 80 91

74 123 124 124 134 78 138 106 130 97 145

93 133 128 96 126 124 125 127 62 127 92

95 118 126 94 127 121 117 124 93 135 156

143 125 120 147 138 72 119 89 81 113 91

133 127 138 122 110 113 100 115 110 135 141

97 127 120 110 107 111 126 132 120 108 148

143 103 92 124 150 86 121 98 74 85 99

Mean and Median

1. The following is the price (in dollars) of a stock (say, CISCO SYSTEMS) checked by a trader several times on a particular day.

139 143 128 138 149 131 143 133

(a) Find the mean price (in dollars) observed by the trader.

(b) Find the median price observed by the trader (in dollars).

2. The following figures refer to the GPA of six students:

3.0 3.3 3.1 3.0 3.1 3.1

(a) Find the median of the GPA.

Measures of Central Tendency

(b) Find the mean of the GPA.

3. The following data give the lifetime (in days) of certain light bulbs.

138 952 980 967 992 197 215 157

(a) Find the mean for the lifetime of these light bulbs.

(b) Find the median for the lifetime of the bulbs.

4. An athlete ran an event 32 times. The following frequency table gives the time taken (in seconds) by the athlete to complete the events.

Time (in seconds) Frequency

11.6 4

11.7 5

11.8 6

11.9 7

12.0 6

12.1 4

Total 32

(a) Compute the mean time taken by the athlete. (Write up to 4 significant digits.)

(b) Find the median time taken by the athlete

5. The following are the weights (in ounces), at birth, of 30 babies born in Lawrence Memorial Hospital in May 2000.

94 105 124 110 119 137 96 110 120 115

104 135 123 129 72 121 117 96 107 80

96 123 124 124 134 78 138 106 130 97

(a) Compute the mean weight, at birth, of the babies.

(b) Using the previous table, compute the median weight, at birth, of the babies.

6. Following is a frequency table for the hourly wages (paid only in whole dollars) of 99 employees in an industry.

Hourly Wages 7 8 9 10 11 12 13 14 15 16 17 18 19

Frequency 1 4 10 4 9 8 6 5 17 19 3 1 2

(a) Compute the mean hourly wage.

(b) Using the previous frequency table, compute the median hourly wage.

7. The following is the frequency table on the number of typos found in a sample of 30 books published by a publisher.

Number of Typos 156 158 159 160 162

Frequency 6 4 5 6 9

(a) Compute the mean number of typos in a book.

(b) Using the previous frequency table, compute the median number of typos found in a book.

8. The following are the lengths (in inches), at birth, of 14 babies born in

Lawrence Memorial Hospital in May 2000.

Length 17 18.5 19 20 21.5

Frequency 2 3 4 3 2

(a) Compute the mean length, at birth, of these babies.

(b) Using the previous table, compute the median length, at birth, of these babies.

Variance and Standard Deviations

1. The following is the price (in dollars) of a stock (say, CISCO SYSTEMS) checked by a trader several times on a particular day.

Mean and Median

138 142 127 137 148 130 142 133

(a) Find the variance of the price (to four decimal places).

(b) Find the standard deviation of the price (to four decimal places).

2. The following figures refer to the GPA of six students:

3.0 3.3 3.1 3.0 3.1 3.1

(a) Find the variance of the GPA (to four decimal places).

(b) Find the standard deviation of the GPA (to four decimal places).

3. The following data give the life time (in days) of certain light bulbs.

938 952 980 967 992 997 915 957

(a) Find the variance for the life time of these bulbs (to four decimal places).

(b) Find the standard deviation for these bulbs (to four decimal places).

4. An athlete ran an event 32 times. The following frequency table gives the time taken (in seconds) by the athlete to complete the events.

Time (in seconds) Frequency

11.6 4

11.7 5

11.8 6

11.9 7

12.0 6

12.1 4

Total 32

(a) Compute the variance for the times taken by the athlete (to four decimal places).

(b) Find the standard deviation for the times taken by the athlete (to four decimal places).

5. The following are the weights (in ounces), at birth, of 30 babies born in Lawrence Memorial Hospital in May 2000.

94 105 124 110 119 137 96 110 120 115

104 135 123 129 72 121 117 96 107 80

96 123 124 124 134 78 138 106 130 97

(a) Compute the variance of the weight, at birth, of the babies.

(b) Compute the standard deviation of the weight, at birth, of the babies.

6. Following is a frequency table for the hourly wages (paid only in whole dollars) of 99 employees in an industry.

Hourly Wages 7 8 9 10 11 12 13 14 15 16 17 18 19

Frequency 11 4 10 4 9 8 6 5 17 19 3 1 2

(a) Compute the variance of the hourly wage.

(b) Compute the standard deviation of the hourly wage.

7. The following is a frequency table on the number of typos found in a sample of 30 books published by a publisher.

Number of Typos 156 158 159 160 162

Frequency 6 4 5 6 9

(a) Compute the variance of the number of typos in a book.

(b) Compute the standard deviation of the number of typos in a book.

8. The following are the lengths (in inches), at birth, of 14 babies born in Lawrence Memorial Hospital in May 2000.

Length 17 18.5 19 20 21.5

Frequency 2 3 4 3 2

(a) Compute the variance of the length, at birth, of these babies.

(b) Compute the standard deviation of the length, at birth, of these babies.