Question

Given the following students' test scores (95, 92, 90, 90, 83, 83, 83, 74, 60, and 50), identify the mean, median, mode, range, variance, and standard deviation for the sample.

Write a 500-750-word summary and analysis discussing the results of your calculations.

State your results for the sample: the mean, median, mode, range, variance, and standard deviation

Explain which method is best for this data set. Why?

Conduct a one sample T-test and interpret the results (use a population mean of 70).

In what situations would this information be useful?

Answer 1

Answer:-

Mean : is the average of given set of data.

Mean = 95 + 92 + 90 + 90 +83 + 83 + 83 + 74 + 60 + 50 / 10 = 800/ 10 = 80

Median:- median is defined as the middle value of a given set of data.

95 92 90 83 83 83 74 60 50

Median = 83

Mode:- Mode is the value that appears maximum times.

Here 83 comes 3 times.

Mode = 83

Range:- is the difference between the smallest and largest values.

Here largest value= 95

Smallest value= 50

Range= 95 - 50= 45

Variance:-the average of the squared differences from the mean.

Here mean is 80.

Now subtract 80 from all given terms.

95 - 80 = 15

92 - 80 = 18

90 - 80 = 10

90- 80 =10

83 - 80 = 3

83 - 80 = 3

83- 80 = 3

74- 80 =-6

60 - 80 = -20

50- 80 = -30

Now find square of all these terms and make summation of all.

225 + 324 + 100 + 100 + 9 +9 + 9+ 36+ 400+900= 2,112

Now divide it by n-1 where n is the number of terms or data point, 10-1=9

Variance= 2,112/ 9=234.67

Standard deviation : measures how far the set of values deviates from mean. It can be found by taking square root of variance.

Standard deviation= 15.32