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Chapter 2: 143SE (page 142)

The amount spent on textbooks for the fall term was recorded for a sample of five university students. The following data were observed: \(400, \)350, \(600, \)525, and $450. Calculate each of the following values for this data:

a.The sample mean

b.The sample median

c.The sample range

d.The standard deviation

Short Answer

Expert verified

a. Mean = $465

b. Median = $450

c. Range = $250

d. Standard Deviation = $99.37

Step by step solution

01

Calculating the mean

x =400, 350, 600, 525, 450

Mean=鈭�蠂n=400+350+600+525+4505=23255=$465

Therefore, the mean value of books is $465.

02

Computing the median

Arranging the data in ascending order,

350, 400, 450, 525, 600

As the sample size is odd, the central value is 450. Therefore, $450 is the median.

03

Finding the range

Maximum value = $600

Minimum value = $350

Range=Max鈥�Min=600鈥�350=$250

Therefore, the range is $250.

04

Estimating the standard deviation

Variance=鈭�蠂鈭�2n鈭�1=400鈭�4652+350鈭�4652+600鈭�4652+525鈭�4652+450鈭�46525鈭�1=4225+13225+18225+3600+2254=395004

=9875

StandardDeviation=Variance=9875=99.37

Therefore, the standard deviation is $99.37.

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