Question

1. A consumer testing laboratory measured the calories per hot dog in 20 brands of beef hot dogs. Here are the results: 186 181 176 149 184 190 158 139 175 148 152 111 141 153 190 157 131 149 135 132 BY HAND Find the five-number summary of this distribution. Be able to explain your procedure. Compute the range and interquartile range. Explain what these numbers tell you about the variability in calories in different brands of all-beef hot dogs. Would a beef hot dog with 175 calories be in the top quarter of the data

Answer 1

Explanation:

Hello!

The five-number summary of a data set includes:

1) Minimum value

2) 1st Quartile (C₁)

3) Median (2nd Quartile) (Me)

4) 3rd Quartile (C₃)

5) Maximum value

First step is to arrange the observations in asending order:

111, 131, 132, 135, 139, 141, 148, 149, 149, 152, 153, 157, 158, 175, 176, 181, 186, 190, 190

From this you can easily detect the min and max od the data set:

Min value: 111

Max value: 190

To detect the quartiles you have to calculate their positions first.

For even samples, the position of each quartile is:

PosC₁= n/4= 20/4= 5

PosMe= n/2= 20/2= 10

PosC₃= (3*n)/4= (3*20)/4= 15

This means that the first quartile will be the 5th observation, the median will be the 10th observation and the third quartile will be the 15th observation:

C₁= 139

Me= 152

C₃= 176

The range of a data set is defined as de difference between the max value and the min value:

R= Max-Min= 190-111= 79

It gives you an idea of how dispersed the data is.

The IQR is the distance between quartile 3 and quartile 1:

IQR= C₃ - C₁= 176-139= 37

Is also a measure of dispersion, it shows how disperse the mid 50% of the data is (arround the Me)

Would a beef hot dog with 175 calories be in the top quarter of the data?

No, the top quarter of the data is determined by the third quartile, in this data set, the top quarter is the values of at least 176 calories. (X≥176)

I hope this helps!