Question

data analysis and probability
constructing a frequency distribution and a histogram
temperatures
(in °f)
97 103 111 98 111 97 105 95
99 106 104 107 101 93 102 112
(a) complete the grouped frequency distribution for
the data. (note that the class width is 4.)
temperatures (in °f) frequency
93 to 96
97 to 100
101 to 104
105 to 108
109 to 112
(b) construct a histogram for the data.
frequency
5
4
3
2
1
0
93 to 96 97 to 100 101 to 104 105 to 108 109 to 112
temperatures (in °f)

Explanation:

Step1: Analyze class 93 - 96

Check which data points (97,103,111,98,111,97,105,95,99,106,104,107,101,93,102,112) lie in 93 - 96. Values: 95, 93. So frequency = 2.

Step2: Analyze class 97 - 100

Data points: 97, 98, 97, 99. Count: 4. Frequency = 4.

Step3: Analyze class 101 - 104

Data points: 103, 101, 102, 104. Count: 4? Wait, 103,101,102,104: that's 4? Wait original data: 103,101,102,104. Wait also check again. Wait data list: 97,103,111,98,111,97,105,95,99,106,104,107,101,93,102,112. So 101,102,103,104: that's 4. So frequency = 4? Wait no, wait 101,102,103,104: four numbers. So frequency 4? Wait no, wait 101,102,103,104: yes. So 4.

Step4: Analyze class 105 - 108

Data points: 105,106,107. Wait 105,106,107: three numbers? Wait 105,106,107: yes. Wait original data: 105,106,107. So frequency = 3.

Step5: Analyze class 109 - 112

Data points: 111,111,112. Wait 111,111,112: three numbers? Wait 111,111,112: yes. Wait original data: 111,111,112. So frequency = 3. Wait no, wait 111,111,112: that's three? Wait 111 (two times), 112: total 3. So:

Wait let's list all data points:

97,103,111,98,111,97,105,95,

99,106,104,107,101,93,102,112.

Now group by classes:

93 - 96: 93,95 → 2

97 - 100: 97,98,97,99 → 4

101 - 104: 101,102,103,104 → 4

105 - 108: 105,106,107 → 3

109 - 112: 111,111,112 → 3

Wait but let's check again:

93-96: 93,95 (values between 93 and 96 inclusive? Wait class width 4, so 93 to 96 (93 ≤ x < 97? Wait maybe the class is 93-96 (inclusive), so 93,95 (93,95 are within 93-96). So 2.

97-100: 97,98,97,99 (97,98,97,99: all between 97-100). So 4.

101-104: 101,102,103,104 (101,102,103,104: between 101-104). So 4.

105-108: 105,106,107 (105,106,107: between 105-108). So 3.

109-112: 111,111,112 (111,111,112: between 109-112). So 3.

Now for the histogram, each bar's height is the frequency. So:

• 93-96: height 2

• 97-100: height 4

• 101-104: height 4

• 105-108: height 3

• 109-112: height 3

Answer:

(a) Frequencies: 93 to 96: 2; 97 to 100: 4; 101 to 104: 4; 105 to 108: 3; 109 to 112: 3.

(b) Histogram bars: 93-96 (height 2), 97-100 (height 4), 101-104 (height 4), 105-108 (height 3), 109-112 (height 3).