**Hint:** Apply direct method in order to calculate the mean of the grouped data.

**Question.1.** The table below shows the time taken by a group of students to complete 100 m dash. Which of these is the mean time taken, in sec, by the group of students to complete the 100 m dash when calculated using direct method?

(a) 18.16

(b) 18.96

(c) 22.7

(d) 23.7

**Question.2.** When calculated using direct method, the mean of the data set shown in the table below is 31. What is the frequency for the class interval 50-60?

(a) 10

(b) 12

(c) 20

(d) 24

**Ans.1.** (d) 23.7**Ans.2.** (b) 12

**Hint:** Apply assumed mean method in order to calculate the mean for a grouped data.

**Question.3.** The table below summarizes the data about the heights of students in a class. When calculated using assumed mean method what is the mean height of students in the class?

(a) 154.33 cm

(b) 154.67 cm

(c) 155.33 cm

(d) 155.67 cm

**Question.4.** Amith grows cucumbers in his farm. He collects some of them and measures their lengths and represents his data as shown below. When calculated using assumed mean method, Amith gets the mean length of the cucumber as 147.25 cm.

Which of the following statement is true?

(a) There are a smaller number of cucumbers of length (140 – 150) mm than of length (120 – 130) mm.

(b) There are a smaller number of cucumbers of length (140 – 150) mm than of length (170 – 180) mm.

(c) There are a greater number of cucumbers of length (140 – 150) mm than of length (150 – 160) mm.

(d) There are a greater number of cucumbers of length (140 – 150) mm than of length (130 – 140) mm.

**Ans.3.** (c) 155.33 cm**Ans.4.** (d) There are a greater number of cucumbers of length (140 – 150) mm than of length (130 – 140) mm.

**Hint:** Compute the mean and mode of the given data in order to interpret the two measures of central tendency.

**Question.5.** A data set is shown. What is the mean and mode of the data shown?

(a) **Mean:** 10; **Mode:** 10.33

(b) **Mean:** 10; **Mode:** 10.67

(c) **Mean:** 11; **Mode:** 10.33

(d) **Mean:** 11; **Mode:** 10.67

**Question.6.** The table below shows the time taken by a group of 40 students to solve a worksheet. Which of the following statements is true?

(a) The mean time taken by the students is more than the sum of time taken by all the students to solve the worksheet.

(b) The time taken by the maximum number of students is less than the mean time taken by the students to solve the worksheet.

(c) The time taken by the maximum number of students is more than the mean time taken by the students to solve the worksheet.

(d) The time taken by the maximum number of students is more than the sum of time taken by all the students to solve the worksheet.

**Ans.5.** (d) Mean: 11; Mode: 10.67**Ans.6.** (b) The time taken by the maximum number of students is less than the mean time taken by the students to solve the worksheet.

**Hint:** Apply formula for the median of a given grouped data in order to calculate missing values of Frequency.

**Question.7.** A grouped data is shown below. If the median of the grouped data is 22.50 and the total frequency is 20, then what is the value of 𝑎?

(a) 1

(b) 2

(c) 4

(d) 5

**Question.8.** The table below shows the time spent by 100 students on exercising every day. If the median time spent by the students on exercising is 26.25 minutes which statement correctly compares the frequencies of the class intervals 0-10 and 40-50?

(a) There are twice as many students who exercise 0- 10 minutes each day as the number of students who exercise 40-50 minutes each day.

(b) There are twice as many students who exercise 40- 50 minutes each day as the number of students who exercise 0-10 minutes each day.

(c) There are thrice as many students who exercise 0- 10 minutes each day as the number of students who exercise 40-50 minutes each day.

(d) There are thrice as many students who exercise 40- 50 minutes each day as the number of students who exercise 0-10 minutes each day.

**Ans.7.** (d) 5**Ans.8.** (b) There are twice as many students who exercise 40- 50 minutes each day as the number of students who exercise 0-10 minutes each day.

**Hint:** Differentiate between mean, median and mode with examples in order to understand most effective measure of central tendency in various cases.

**Question.9.** A grouped data is shown below: Which of the following is the most effective measure of central tendency?

(a) Mean because the data has extreme data points.

(b) Median because the data has extreme data points.

(c) Mean because the data has no extreme data points.

(d) Median because the data has no extreme data points.

**Question.10.** The table below shows the age of people attending a musical concert. If five more people of age 21 yrs., 32 yrs., 35 yrs., 44 yrs., and 11 yrs. attend the concert, which statement describes the central tendency of the new data?

(a) The central tendency of the data increases by 0.1 as the mean increases by 0.1.

(b) The central tendency of the data increases by 0.1 as the median increases by 0.1.

(c) The central tendency of the data increases by 0.2 as the mean increases by 0.2.

(d) The central tendency of the data increases by 0.2 as the median increases by 0.2.

**Ans.9.** (b) Median because the data has extreme data points.**Ans.10.** (d) The central tendency of the data increases by 0.2 as the median increases by 0.2.

**Hint:** Derive the co-ordinates to plot on the graph in order to represent the two ogives.

**Question.11.** The table below shows the heights of plants in Pranay’s backyard. Which of the following are the coordinates of less than ogive curve?

(a) (0, 10), (50, 35), (100, 65), (150, 93), (200, 105), (250, 119)

(b) (10, 0), (35, 50), (65, 100), (93, 150), (105, 200), (119, 250)

(c) (10, 50), (35, 100), (65, 150), (93, 200), (105, 250), (119, 300)

(d) (50, 10), (100, 35), (150, 65), (200, 93), (250, 105), (300, 119)

**Question.12.** The table below shows the age group of 50 women members of a club.Given that y-z= 1, Aruna and Anjali wrote the coordinates of less than ogive curve and more than ogive curve respectively as shown below.**Aruna:** (20, 2), (25, 13), (30, 29), (35, 39), (40, 46), (45, 50)**Anjali:** (20, 50), (25, 48), (30, 38), (35, 22), (40, 11), (45, 4)

Who is/are correct?

(a) Only Aruna

(b) Only Anjali

(c) Both of them

(d) Neither of them

**Ans.11.** (d) (50, 10), (100, 35), (150, 65), (200, 93), (250, 105), (300, 119)**Ans.12.** (d) Neither of them

**Hint:** Graph both ogives for the data obtained in order to determine the median of the given grouped data for.

**Question.13.** A grouped data is shown below. Which graph shows the median of the data?

(a) (b) (c) (d)

**Question.14.** The table below shows the number of hours a group of 80 students sleep every day.Given that b-a= 8, which of the following represents the median number of hours the group of students sleep?

(a) (b) (c) (d)

**Ans.13.** (c) **Ans.14.** (a)