Question

An experiment is conducted to observe the room temperature. Assume the temperature can vary from 0 oF to 100 oF. A collection of 6 measurements of temperature in a classroom during May is given below.

Meas.# 1 2 3 4 5 6

Temperature 34 79 91 38 46 20 oF

(a) Define the sample space for the measurements.

(b) Find at least two statistical measures for location. Indicate which one is preferred.

(c) Find the variance and standard deviation.

(d) Construct the boxplot and indicate 1) the normal range of data and 2) if there is any outlier.

Answer 1

A)the sample space is all the temperature measurements Which ranges from 0 to 100 degree F

B) 2 statistical measurement are mean and median .

= Mean = (34+ 79 +91+ 38+ 46+ 20)/6

= 308/6 = 51.33

Median = middle most value of sorted data

So sorted data is 20,34,38,46,79,91

So median =( 3rd + 4th data )/2 =( 38+46)/2 = 42

Mean is the most preferred measure temperature because it is based on all the values

C)so standard deviation =

root( variance) = root(637.88889) = 25.25 ( approx)

D)

Median: 42
Minimum: 20
Maximum: 91
First quartile: 30.5
Third quartile: 82
Interquartile Range: 51.5 {Q3-Q1}

Range is = 91-20 =71

Upper fence= Q3+IQR×1.5 = 82 + 1.5×51.5 = 159.25

Lower fence = Q1-1.5×51.5= -46.75

So none of the value is above upper fence and below lower fences so no outliers are there