CBSE Class 10 Mathematics Statistics Worksheet Set 09

SECTION A

Question. Choose and write the correct option in the following questions.
(i) A data set is shown.
Class Interval: 4–6, 6–8, 8–10, 10–12, 12–14, 14–16, 16–18
Frequency: 2, 6, 20, 28, 12, 10, 2
What is the mean and mode of the data shown?
(a) Mean: 11; Mode: 10.33
(b) Mean: 11; Mode: 10.67
(c) Mean: 10; Mode: 10.33
(d) Mean: 10; Mode: 10.67
Answer: (b) Mean: 11; Mode: 10.67

Question. A grouped data is shown below:
Class Interval: 0–15, 15–30, 30–45, 45–60, 60–75, 75–90
Frequency: 2, 26, 32, 42, 28, 30
Which of the following is the most effective measure of central tendency?
(a) Mean because the data has extreme data points.
(b) Mean because the data has no extreme data points.
(c) Median because the data has extreme data points.
(d) Median because the data has no extreme data points.
Answer: (c) Median because the data has extreme data points.

Question. In the formula \( \bar{x} = a + \frac{\sum f_id_i}{\sum f_i} \) for finding the mean of a grouped data, \( d_i \)'s are deviations from \( a \) of
(a) lower limits of the classes
(b) upper limits of the classes
(c) mid-points of the classes
(d) frequencies of the class marks
Answer: (c) mid-points of the classes

Question. Solve the following questions. (2 x 1 = 2)
(i) The mean of 11 observations is 50. If the mean of first 6 observations is 49 and that of the last six observations is 52, what is the value of 6th observation?
(ii) Find the median of first 10 prime numbers.
Answer: (i) Sum of 11 observations \( = 11 \times 50 = 550 \)
Sum of first 6 observations \( = 6 \times 49 = 294 \)
Sum of last 6 observations \( = 6 \times 52 = 312 \)
Value of 6th observation \( = (294 + 312) - 550 \)
\( \implies \) \( 606 - 550 = 56 \)
(ii) First 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Median \( = \frac{11 + 13}{2} = 12 \)

SECTION B

Question. Find the mean of the following distribution:
\( x \): 4, 6, 9, 10, 15
\( f \): 5, 10, 10, 7, 8
Answer: \( \sum f_i = 40 \)
\( \sum f_i x_i = (4 \times 5) + (6 \times 10) + (9 \times 10) + (10 \times 7) + (15 \times 8) \)
\( = 20 + 60 + 90 + 70 + 120 = 360 \)
Mean \( = \frac{360}{40} = 9 \)

Question. If \( x_i \)'s are the mid-points of the class intervals of a grouped data. \( f_i \)'s are the corresponding frequencies and \( \bar{x} \) is the mean, then find \( \sum f_i(x_i - \bar{x}) \).
Answer: \( \sum f_i(x_i - \bar{x}) = \sum f_i x_i - \bar{x} \sum f_i \)
\( = \sum f_i x_i - \left( \frac{\sum f_i x_i}{\sum f_i} \right) \sum f_i = \sum f_i x_i - \sum f_i x_i = 0 \)

Question. If the mean of the following distribution is 27, find the value of \( p \).
Classes: 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 8, \( p \), 12, 13, 10
Answer: \( p = 7 \)

Question. Following table shows the weight of 12 students:
Weight (in kgs): 67, 70, 72, 73, 75
Number of students: 4, 3, 2, 2, 1
Find the mean weight of the students.
Answer: Total weight \( = (67 \times 4) + (70 \times 3) + (72 \times 2) + (73 \times 2) + (75 \times 1) \)
\( = 268 + 210 + 144 + 146 + 75 = 843 \)
Mean weight \( = \frac{843}{12} = 70.25 \text{ kg} \)

Question. Calculate the median from the following data:
Rent (in Rs.): 1500–2500, 2500–3500, 3500–4500, 4500–5500, 5500–6500, 6500–7500, 7500–8500, 8500–9500
Number of tenants: 8, 10, 15, 25, 40, 20, 15, 7
Answer: Rs. 5,800

Question. Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
Age (in years): 0–10, 10–20, 20–30, 30–40, 40–50
Number of persons: 5, 25, \( f \), 18, 7
Answer: \( f = 25 \)

Question. Find the median for the following distribution.
Classes: 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90
Frequency: 10, 8, 12, 24, 6, 25, 15
Answer: 58.33 (approx)

Question. 50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below:
Distance (in m): 0–20, 20–40, 40–60, 60–80, 80–100
No. of students: 6, 11, 17, 12, 4
Calculate the median distance by using the formula for median.
Answer: 49.41 m

Question. The following distribution gives the daily income of 50 workers of a factory:
Daily income (in Rs.): 100–120, 120–140, 140–160, 160–180, 180–200
Number of workers: 12, 14, 8, 6, 10
Find the median.
Answer: 138

Question. An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table:
Number of seats: 100–104, 104–108, 108–112, 112–116, 116–120
Frequency: 15, 20, 32, 18, 15
Determine the mean number of seats occupied over the flights.
Answer: 110 seats

Question. The marks obtained by 100 students of a class in an examination are given below.
Marks: 0-5, 5-10, 10-15, 15-20, 20-25, 25-30, 30-35, 35-40, 40-45, 45-50
No. of students: 2, 5, 6, 8, 10, 25, 20, 18, 4, 2
Find median.
Answer: 29.5