Chapter 15 - Statistics
Practice set 54
1. The daily rainfall for each day of a week in a certain city is given in millimetres. Find the average rainfall during the week.
9, 11, 8, 20, 10, 16, 12
Solution:
We know that,
Average = \( \large \frac{\text { Sum of all scores in the given data }}{\text { Total number of scores }}\)
∴ Average rainfall during the week = \( \large \frac{\text { Sum of rainfall of each day of the week }}{\text { Total number of days }}\)
∴ Average rainfall during the week = \(\large \frac{9\, +\, 11\, +\, 8\, +\, 20\, +\, 10\, +\, 16\, +\, 12}{\text {7}}\)
∴ Average rainfall during the week = \(\large \frac{87}{7}\)
∴ Average rainfall during the week = 12.285 ≈ 12.29 mm
Ans: The average rainfall during the week is 12.29 mm
2. During the annual function of a school, a Women’s Self-help Group had set up a snacks stall. Their sales every hour were worth ₹ 960, ₹ 830, ₹ 945, ₹ 800, ₹ 847, ₹ 970 respectively. What was the average of the hourly sales?
Solution:
We know that,
Average = \( \large \frac{\text { Sum of all scores in the given data }}{\text { Total number of scores }}\)
∴ Average hourly sales = \( \large \frac{\text { Sum of sales every hour}}{\text { Total number of hours }}\)
∴ Average hourly sales = \(\large \frac{960\, +\, 830\, +\, 945\, +\, 800\, +\, 847\, +\, 970}{\text {6}}\)
∴ Average hourly sales = \(\large \frac{5352}{6}\)
∴ Average hourly sales = ₹ 892
Ans: The average of the hourly sales was ₹ 892.
3. The annual rainfall in Vidarbha in five years is given below. What is the average rainfall for those 5 years ?
900 mm, 650 mm, 450 mm, 733 mm, 400 mm
Solution:
We know that,
Average = \( \large \frac{\text { Sum of all scores in the given data }}{\text { Total number of scores }}\)
∴ Average rainfall for 5 years = \( \large \frac{\text { Sum of annual rainfall in 5 years}}{\text { Total number of years }}\)
∴ Average rainfall for 5 years = \(\large \frac{900\, +\, 650\, +\, 450\, +\, 733\, +\, 400}{\text {5}}\)
∴ Average rainfall for 5 years = \(\large \frac{3133}{5}\)
∴ Average rainfall for 5 years = 626.6 mm
Ans: The average rainfall in Vidarbha for 5 years was 626.6 mm.
4. A farmer bought some sacks of animal feed. The weights of the sacks are given below in kilograms. What is the average weight of the sacks ?
49.8, 49.7, 49.5, 49.3, 50, 48.9, 49.2, 48.8
Solution:
We know that,
Average = \( \large \frac{\text { Sum of all scores in the given data }}{\text { Total number of scores }}\)
∴ Average weight of the sacks = \( \large \frac{\text { Sum of weight of each sack}}{\text { Total number of sacks }}\)
∴ Average weight of the sacks = \(\large \frac{49.8\, +\, 49.7\, +\, 49.5\, +\, 49.3\, +\, 50\, +\, 48.9\, +\, 49.2\, +\, 48.8}{\text {8}}\)
∴ Average weight of the sacks = \(\large \frac{395.2}{8}\)
∴ Average weight of the sacks = 49.4 kg
Ans: The average weight of the sacks is 49.4 kg.
Practice set 55
1. The height of 30 children in a class is given in centimetres. Draw up a freqency table of this data.
131, 135, 140, 138, 132, 133, 135, 133, 134, 135, 132, 133, 140, 139, 132, 131, 134, 133, 140, 140, 139, 136, 137, 136, 139, 137, 133, 134, 131, 140
Solution:
| Height of children (cm) | Tally marks | Frequency |
|---|---|---|
131 | ||| | 3 |
132 | ||| | 3 |
133 | \(\require{cancel} \cancel {||||}\) | 5 |
134 | ||| | 3 |
135 | ||| | 3 |
136 | || | 2 |
137 | || | 2 |
138 | | | 1 |
139 | ||| | 3 |
140 | \(\require{cancel} \cancel {||||}\) | 5 |
N = 30 |
2. In a certain colony, there are 50 families. The number of people in every family is given below. Draw up the frequency table.
5, 4, 5, 4, 5, 3, 3, 3, 4, 3, 4, 2, 3, 4, 2, 2, 2, 2, 4, 5, 1, 3, 2, 4, 5, 3, 3, 2, 4, 4, 2, 3, 4, 3, 4, 2, 3, 4, 5, 3, 2, 3, 2, 3, 4, 5, 3, 2, 3, 2
Solution:
| Number of People in each family | Tally marks | Frequency |
|---|---|---|
1 | | | 1 |
2 | \(\require{cancel} \cancel {||||}\) \(\require{cancel} \cancel {||||}\) ||| | 13 |
3 | \(\require{cancel} \cancel {||||}\) \(\require{cancel} \cancel {||||}\) \(\require{cancel} \cancel {||||}\) | | 16 |
4 | \(\require{cancel} \cancel {||||}\) \(\require{cancel} \cancel {||||}\) ||| | 13 |
5 | \(\require{cancel} \cancel {||||}\) || | 7 |
N = 50 |
3. A dice was cast 40 times and each score noted is given below. Draw up a frequency table for this data.
3, 2, 5, 6, 4, 2, 3, 1, 6, 6, 2, 3, 5, 3, 5, 3, 4, 2, 4, 5, 4, 2, 6, 3, 3, 2 4, 3, 3, 4, 1, 4, 3, 3, 2, 2, 5, 3, 3, 4
Solution:
| Number on top face of the dice | Tally marks | Frequency |
|---|---|---|
1 | || | 2 |
2 | \(\require{cancel} \cancel {||||}\) ||| | 8 |
3 | \(\require{cancel} \cancel {||||}\) \(\require{cancel} \cancel {||||}\) ||| | 13 |
4 | \(\require{cancel} \cancel {||||}\) ||| | 8 |
5 | \(\require{cancel} \cancel {||||}\) | 5 |
6 | |||| | 4 |
N = 40 |
4. The number of chapatis that 30 children in a hostel need at every meal is given below. Make a frequency table for these scores.
3, 2, 2, 3, 4, 5, 4, 3, 4, 5, 2, 3, 4, 3, 2, 5, 4, 4, 4, 3, 3, 2, 2, 2, 3, 4, 3, 2, 3, 2
Solution:
| Number on top face of the dice | Tally marks | Frequency |
|---|---|---|
2 | \(\require{cancel} \cancel {||||}\) |||| | 9 |
3 | \(\require{cancel} \cancel {||||}\) \(\require{cancel} \cancel {||||}\) | 10 |
4 | \(\require{cancel} \cancel {||||}\) ||| | 8 |
5 | ||| | 3 |
N = 30 |