Answer to Question #164139 in Statistics and Probability for MUSAH ABDUL-JAWAL

Question

Q2: Group Frequency 

The length, in mm, of 48 rubber tree leaves are given below: 

137 152 127 147 141 157 132 153 166 147 136 134 

146 142 162 169 149 135 166 157 141 146 147 148 

163 133 148 150 136 127 162 152 143 138 142 153 

145 154 144 126 139 126 158 147 136 144 159 161 

Create a group frequency table for this data using sturge’s rule as a guide to find the number of intervals 

Q3: Group Frequency 

A Statistics test is marked out of 60. Here are the marks for the 65 students:

 26 11 21 35 44 23 37 26 11 21 35 44 23 

37 26 11 21 35 44 23 37 16 42 11 47 59 

45 16 13 18 16 42 11 47 59 45 16 13 18 

16 42 11 47 59 45 16 13 18 19 25 15 32 

54 8 38 42 53 19 25 15 32 54 8 38 42 

a. Construct a grouped frequency table for the data using the 2 to k rule as guide to find  the number of intervals. 

b. What percentages of the class scored above 40 marks? 

Q4: Simple Frequency and Bar Chart 

James asked his friends their favourite colours. They mention 

Green Blue Red Green Blue Blue Green 

Red Blue White Blue Green Red Green 

Blue Red Blue Green Red Green 

a. Construct a frequency table for the favourite colour data 

b. Represent the information on a bar chart

Answer 1

Q2

n = 48

Sturge's rule: the number of groups or classes is k = 1 + 3.322 log(n)

Thus k = 1 + 3.322 log48 = 7

the lowest value is 126

the highest value is 169

range R = the highest value – the lowest value = 169 – 126 = 43

the class width = $\frac{R}{k}=\frac{43}{7}=6$

thus we have:

Q3

n = 65

According to 2^k rule, 2^k > n, where k is the number of classes and n is the number of data points.

2^k > 65

Therefore the number of classes is k = 7

the lowest value is 8

the highest value is 59

range R = the highest value – the lowest value = 59 – 8 = 51

the class width = $\frac{R}{k}=\frac{51}{7}=7$

thus we have:

What percentages of the class scored above 40 marks?

There are 20 students that scored above 40 marks thus:

$\frac{20}{65}\cdot100\%=31\%$

Q4