Measures of Central Tendency for Grouped Data

Q. The following table 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 mean, mode and median of the above data.

Q.

Which of the following is not a measure of central tendency?

(a) Mean (b) Mode (c) Median (d) Range

Q.

The following number of goals were scored by a team in a series of $10$ matches: $2,3,4,5,0,1,3,3,4,3$.Find the mean, median, and mode of these scores.

Q. If the preceding and succeeding classes of the modal class have the same frequency, then the mode will be theof the modal class.

1. midpoint
2. upper limit
3. lower limit

Q.

A researcher wanted to estimate the average amount of money spent on extracurricular activities per school in a certain region.

The researcher randomly selected 20 public schools and 20 private schools in the region to use for a sample.

Which of the following best describes the type of sample that was taken?

1. A census

2. A cluster sample

3. A convenience sample

4. A simple random sample

5. A stratified random sample

Q. What does the l in mode $=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$ stand for?

Q.

If the preceding and succeeding classes of the modal class have the same frequency, then the mode will be at the midpoint of the modal class.

1. False

2. True

Q.

Heights of students of Class X are given in the following frequency distribution :
$\begin{array}{cccccc}\text{Marks}& 150-155& 155-160& 160-165& 165-170& 170-175\\ \text{Number of}& & & & & \\ \text{students}& 15& 8& 20& 12& 5\end{array}$
Find the modal height.
Also, find the mean height. Compare and interpret the two measures of central tendency.

Q.

Match the following columns:

$\begin{array}{cc}ColumnI& ColumnII\\ \left(a\right)Themostfrequentvalueinadatais& \\ knownas........& \left(p\right)standarddeviation\\ \left(b\right)whichofthefollowingcannot& \\ bedeterminedgraphicallyoutof& \\ mean,modeandmedian?& \left(q\right)median\\ \left(c\right)Anogiveisusedtodetermine.......& \left(r\right)mean\\ \left(d\right)Outofmean,mode,medianand& \\ standarddeviation,whichisnota& \\ measureofcentraltendency?& \left(s\right)mode\end{array}$

Q. In a moderately skewed distribution, if the values of mean and mode are 10k and 7k respectively, then its median is

1. 6k
2. 7k
3. 8k
4. 9k

Q. Use the empirical relationship and find the value of mode when the value of median and mean are 6 and 7 respectively.

1. 4
2. 3
3. 6
4. 7

Q.

Which of the following expressions is used to determine the mode?

1. $l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

2. $l+\left(\frac{f_1-f_0}{f_1-f_0-f_2}\right)\times h$

3. $l+\left(\frac{f_1-f_0}{2f_2-f_0-f_1}\right)\times h$

4. $\frac{{2f}_1-f_0}{{2f}_1-f_0-f_2}$

Q.

Find the mode of the following data.
$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 6& 7& 11& 9& 7\end{array}$$

Q.

Which of the following represents an empirical relationship between Median, Mode and Mean?

1. 3 Mode= Median + 2 Mean

2. Mode =3 Median - 2 Mean

3. 3 Mean= Median + 2 Mode

4. can't say.

Q.

Find the mode of the following data.
$$\begin{array}{cccccc}Classinterval& 100-120& 120-140& 140-160& 160-180& 180-200\\ Frequency& 10& 13& 8& 7& 12\end{array}$$

Q. If the preceding and succeeding classes of the modal class have the same frequency, then the mode will be the _______ .

1. midpoint of the modal class
2. upper limit of the modal class
3. lower limit of the modal class
4. midpoint of the preceding class

Q. The following frequency distribution gives the monthly consumption of electricity of $68$ consumers of a locality. Find the median, mean and mode of the data and compare them.
$\begin{array}{cc}\text{Monthly consumption}& \text{Number of consumers}\\ \text{(in units)}& \\ 65-85& 4\\ 85-105& 5\\ 105-125& 13\\ 125-145& 20\\ 145-165& 14\\ 165-185& 8\\ 185-205& 4\end{array}$

Q.

The following data shows the warranty period of different components. Find the modal warranty period.

$$\begin{array}{ccccccc}\text{Warranty period (years)}& 0-1& 1-2& 2-3& 3-4& 4-5& 5-6\\ \text{Number components}& 6& 10& 16& 25& 16& 20\end{array}$$

1. 3
2. 3.25
3. 3.5
4. 4.5

Q. Assertion: (A) In a graphical representation, if P times the distance between the median and mean is thrice the distance between mode and mean, then the value of p is 9.
Reason: (R) Mode= 3 Median - 2 Mean
Which of the following is true?

1. (A) and (R) are true and (R) is the correct explanation of (A)
2. (A) is false and (R) is the correct explanation of (A)
3. (A) is true and (R) is false
4. Both (A) and (R) are false

Q.

Find the mode of the following data.
$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 8& 10& 14& 10& 8\end{array}$$

Q.

Find the mode of the following data.
$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 10& 9& 8& 17& 6\end{array}$$

Q. For which data set, the mean is not a good representative measures of central tendency.

1. There are 7 classes with the below frequencies.
   
   {10, 12, 15, 17, 14, 15, 17}
2. There are 6 classes with the below frequencies.
   
   {2, 20, 25, 17, 19, 22}
3. There are 7 classes with the below frequencies.
   
   {5, 7, 5, 6, 4, 5, 7}
4. There are 6 classes with the below frequencies.
   
   {17, 20, 25, 17, 19, 22}

Q. If the median and mean of a given data are $\frac{1}{x}$ and $\frac{1}{y}$ respectively, then its mode is

1. $\frac{3y-2x}{xy}$
2. $\frac{3y+2x}{xy}$
3. $\frac{x+y}{2xy}$
4. $\frac{y-2x}{3xy}$

Q. If mean and mode for a certain data are 37 and 52 respectively, then the median of the data is

1. 37
2. 48
3. 42
4. 52

Q.

Which of the following measures of central tendency is influenced by extreme values?

(a) Mean (b) Mode (c) Median (d) None of these

Q.

Which of the following is a measure of central tendency?

1. Frequency

2. Mean

3. Class interval

4. Class

Q. If the preceding and succeeding classes of the modal class have the same frequency, then the mode will be theof the modal class.

1. midpoint
2. upper limit
3. lower limit

Q.

6. For more than ogive the x-axis represents :

(a) upper limits of class-intervals (b) mid-values of class-intervals

(c) lower limits of class-intervals (d) frequency

7. Ogive is the graph of :

(a) lower limits and frequency (b) upper limits and frequency

(c)lower/upper limits and cumulative frequency (d) none of these

8. The curve less than ogive is always :

(a)ascending (b) descending

(c) sometimes ascending and sometimes descending (d) none of these

9. If mode = 80 and mean = 110, then the median is

(a)110 (b)120

(c)100 (d)90

10. The mean of the following data is : 45, 35, 20, 30, 15, 25, 40 :

(a) 15 (b) 25

(c) 35 (d) 30

11 . The mean and median of a data are 14 and 15 respectively. The value of mode is (a) 16 (b) 17

(c) 13 (d) 18

12 . For a given data with 50 observations the less than ogive and the more then ogive intersect at (15.5, 20). The median of the data is :

(a) 4.5 (b) 20

(c) 50 (d) 15.5

13. Which of the following is not a measure of central tendency ?

(a) Mean (b) Median

(c) Range (d) Mode

14. The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its :

(a)mean (b) median

(c) mode (d) all the three above

15. The measures of central tendency which cant be found graphically is

(a) mean (b) median

(c) mode (d) none of these

Q. If the preceding and succeeding classes of the modal class have the same frequency, then the mode will be theof the modal class.

1. midpoint
2. upper limit
3. lower limit

Q.

Which of the following expressions is used to determine the mode?

1. $l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

2. $l+\left(\frac{f_1-f_0}{f_1-f_0-f_2}\right)\times h$

3. $l+\left(\frac{f_1-f_0}{2f_2-f_0-f_1}\right)\times h$

4. $\frac{{2f}_1-f_0}{{2f}_1-f_0-f_2}$