Question

The following data represents the amount of money that individuals spent on gifts for Mother's Day

$110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

Refer to the Exhibit Mother's Day Gifts.

Calculate descriptive statistics for this sample using Excel. More specifically, find the following statistics (you can use either the Data Analysis tool or find these statistics with corresponding Exel functions. Notice that percentiles and the z-score are not provided by the Data Analysis (you will need to additionally calculate them)):

Mean

Median

Mode

Variance

Standard Deviation

Range

40th percentile

z-score for the spending of $137

In your own words, interpret the value of the median you calculated.

In your own words, how do you interpret the value of the mode you calculated in Excel.

In your own words, interpret the value of the 40th percentile? (one line answer)

In your own words, interpret the z-score for the spending of $137?

Answer 1

The summary statistics of the Excel output is :

40th Percentile of the data :

P₄₀ = 40(n+1)100 =5.2th value

P₄₀ = 134+0.2(137-134) =134.6

Z score , When X = 137

a) Interpretation of Median : The value that divides the data into two equal parts, the middlemost value of the arranged data is median. Here we have median 139, that means 6 data values are below this value and 6 data values are above this value.

b) Mode : The mode of the given data is zero, because none of the values repeats in the data.

c) 40th Percentile : 40 percent of the individuals spents less than $134.6 on gifts for Mother's Day.

d) Z score - The amout $137 is 0.201 standard deviation below the mean .