2.118 - Elementary Statistics

Question

Residential Energy Consumption. Refer to the energy consumption data given in Exercise 2.84.

a. Construct a table similar to table $2.14$ for the data, based on the classes specified in Exercise 2.84. Interpret your results.

b. Construct an ogive for the data.

Step-by-Step Solution

Answer

(a) The Construct a table similar to table table for the data is shown in figure,

Class	frequency	Relative frequency
$40-49$	$1$	$0.02$
$50-59$	$7$	$0.14$
$60-69$	$7$	$0.14$
$70-79$	$3$	$0.06$
$80-89$	$6$	$0.12$
$90-99$	$10$	$0.2$
$100-109$	$5$	$0.1$
$110-119$	$4$	$0.08$
$120-129$	$2$	$0.04$

$130-139$	$3$	$0.06$
$140-149$	$0$	$0$
$150-159$	$2$	$0.04$

b. Construct an ogive for the data graph is shown in.

Part (a) Step 1: Given Information

Given in the question that to refer to the energy consumption data given in exercise 2.84

We have construct a table similar to table $2.14$ for the data.

Part (a) Step 2: Explanation

Based on the outcome of the previous exercise, the table will be 

Class	Frequency	Relative frequency
$40-49$	$1$	$0.02$
$50-59$	$7$	$0.14$
$60-69$	$7$	$0.14$
$70-79$	$3$	$0.06$
$80-89$	$6$	$0.12$
$90-99$	$10$	$0.2$
$100-109$	$5$	$0.1$
$110-119$	$4$	$0.08$
$120-129$	$2$	$0.04$

$130-139$	$3$	$0.06$
$140-149$	$0$	$0$
$150-159$	$2$	$0.04$

Part (b) Step 1: Given Information

We have to refer exercise 2.84 and construct an ogive for the data.

Part (b) Step 2: Explanation

The cumulative relative frequency is calculated by dividing the overall frequency of 50 by the cumulative frequency. Then,

Lower class limit	Cumulative frequency	Cumulative relative frequency
$40$	$0$	$0$
$50$	$1$	$0.02$
$60$	$8$	$0.16$
$70$	$15$	$0.3$
$80$	$18$	$0.36$
$90$	$24$	$0.48$
$100$	$34$	$0.68$
$110$	$39$	$0.78$
$120$	$43$	$0.86$

$130$	$45$	$0.9$
$140$	$48$	$0.96$
$150$	$48$	$0.96$
$160$	$50$	$1$

Part (b) Step 3: Explanation

As indicated below, add the above points to the graphs and connect them with a straight line.