Q. 2.119 - Elementary Statistics

Question

Clocking the Cheetah. Refer to the speed data given in Exercise $2.89$.

a. Construct a table similar to Table $2.14$ for the data, based on the classes specified in Exercise 2.89. Interpret your results.

b. Construct an ogive for the data.

Step-by-Step Solution

Answer

(a). The construct a table similar to table for the data is shown in figure.

Class	Frequency	Relative frequency
$52-<54$	$2$	$0.057$
$54-<56$	$5$	$0.143$
$56-<58$	$6$	$0.171$
$58-<60$	$8$	$0.229$
$60-<62$	$7$	$0.2$
$62-<64$	$3$	$0.086$
$64-<66$	$2$	$0.057$
$66-<68$	$1$	$0.029$
$68-<70$	$0$	$0$

$70-<72$	$0$	$0$
$72-<74$	$0$	$0$
$74-<76$	$1$	$0.029$
Total	$35$	$1$

(b) The construct an ogive for the data graph is shown in figure.

Part (a) Step 1: Given Information

We have to refer the speed data given in exercise 2.89. Then construct a table similar to table $2.14$ for the data.

Part (a) Step 2: Explanation

Based on the outcome of the previous exercise,

Class	Frequency	Relative frequency
$52-<54$	$2$	$0.057$
$54-<56$	$5$	$0.143$
$56-<58$	$6$	$0.171$
$58-<60$	$8$	$0.229$
$60-<62$	$7$	$0.2$
$62-<64$	$3$	$0.086$
$64-<66$	$2$	$0.057$
$66-<68$	$1$	$0.029$
$68-<70$	$0$	$0$

$70-<72$	$0$	$0$
$72-<74$	$0$	$0$
$74-<76$	$1$	$0.029$
Total	$35$	$1$

Part (b) Step 1: Given Information

Given in the question to refer exercise 2.89. We have to construct an ogive for the data. 

Part (b) Step 2: Explanation

The cumulative relative frequency is calculated by dividing the overall frequency of 35 by the cumulative frequency. Then

Lower class limit	Cumulative frequency	Cumulative relative frequency
$52$	$0$	$0$
$54$	$2$	$0.0571$
$56$	$7$	$0.2$
$58$	$13$	$0.3714$
$60$	$21$	$0.6$
$62$	$28$	$0.8$
$64$	$31$	$0.8857$
$66$	$33$	$0.9429$
$68$	$34$	$0.9714$

$70$	$34$	$0.9714$
$72$	$34$	$0.9714$
$74$	$34$	$0.9714$
$76$	$35$	$1$

Part (b) Step 3: Explanation

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