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Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

The following is the distribution of weekly wages of workers in a factory. Calculate the arithmetic mean of the distribution.

Weekly Wages (Rs.) No. of Workers
$240-269$ $7$
$270-299$ $19$
$300-329$ $27$
$330-359$ $15$
$360-389$ $12$
$390-419$ $12$
$420-449$ $8$
  1. $352.3$
  2. $344.5$
  3. $226.7$
  4. $336.7$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Class Intervals Mid-values (x) Frequency(f) fx
$240-269$ $254.5$ $7$ $1,781.5$
$270-299$ $284.5$ $19$ $5,405.5$
$300-329$ $314.5$ $27$ $8,491.5$
$330-359$ $344.5$ $15$ $5,167.5$
$360-389$ $374.5$ $12$ $4,494$
$390-419$ $404.5$ $12$ $4,854$
$420-449$ $434.5$ $8$ $3,476$
$\displaystyle\sum f=100$ $\displaystyle\sum fx=33,670$

Arithmetic mean $=33,670/100=336.7$.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

The mean weight of $98$ students is found to be $50$ lbs. It is later discovered that the frequency of the class interval $(30-40)$ was wrongly taken as $8$ instead of $10$. Calculate the correct mean.

  1. $49.00$
  2. $49.50$
  3. $49.25$
  4. $49.70$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Incorrect mean,
$X=50$kg.
$\displaystyle\sum f _i=98$
Incorrect X$=\displaystyle\frac{Incorrect \displaystyle\sum f _iX _i}{\displaystyle\sum f _i}$
$50=\displaystyle\frac{Incorrect \displaystyle\sum f _iX _i}{98}$
$\therefore$ Incorrect $\displaystyle\sum f _iX _i=98\times 50=4900$
Now, Correct $\displaystyle\sum f _iX _i=$Incorrect $\displaystyle\sum f _iX _i-(8\times 35)+(10\times 35)$
Note, the class-mark of class interval $(30-40)$ is $35$ and for the calculation of the mean, we consider class marks.
Correct $\displaystyle\sum f _iX _i=4900-280+350$
$=4,970$
Also, Correct $\displaystyle\sum f _i=98+2=100$
$\therefore$ Correct Mean$=\displaystyle\frac{Correct \displaystyle\sum f _iX _i}{Correct \displaystyle\sum f _i}$
$=\displaystyle\frac{4970}{100}$
$X=49.70$lbs.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

Consider the following frequency distribution.

Class Intervals $0-10$ $10-20$ $20-30$ $30-40$
Frequency $8$ $10$ $12$ $15$

Arithmetic mean $=$?

  1. $39.65$
  2. $22.55$
  3. $32.55$
  4. $23.56$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Class Intervals Mid-values(x) Frequency(f) fx
$01-0$ $5$ $8$ $40$
$10-20$ $15$ $10$ $150$
$20-30$ $25$ $12$ $300$
$30-40$ $35$ $15$ $525$
$\displaystyle\sum f=45$ $\displaystyle\sum fx =1,015$

Arithmetic mean $=1,015/45=22.55$.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

Coefficient of variation of a distribution is $60$ and its standard deviation is $21$, then its arithmetic mean is?

  1. $36$
  2. $37$
  3. $35$
  4. $38$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The coefficient of variation (CV) is calculated as (Standard Deviation / Mean) * 100. Rearranging the formula gives Mean = (Standard Deviation / CV) * 100. Substituting the given values: Mean = (21 / 60) * 100 = 0.35 * 100 = 35.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

Arithmetic mean for grouped data can be calculated by _________.

  1. direct method

  2. assumed mean method

  3. step deviation method

  4. all of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class. 

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

What needs to be done for calculating mean for a continuous series?

  1. Mid-points of various class intervals are taken

  2. Lower class limits are taken

  3. Upper class limits are taken

  4. A or B or C
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To calculate the mean of a continuous series, mid points of the various class intervals is taken. For example, if the class is like 10-20 then before calculating the mean mid point that is 15 is calculated for the whole series which is added and divided by the number of terms in order to ascertain the mean. 

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

For grouped data, Arithmetic mean by Direct Method =

  1. sfX / sf

  2. sd / N

  3. sX / N

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean for grouped data like direct method where all the data are multiplied with their respective frequencies and then added up which are then divided by the summation of the frequencies or number of figures in the data in order to ascertain the mean. The formula is sfX/ sf where sfd is the summation of frequency multiplied by X for all figures and sf is the frequency or the number of element in the given data. 

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

For grouped data, Arithmetic mean by Assumed Mean Method =

  1. A + sd/N

  2. A + sfd/sf

  3. sfX/sf

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In assumed mean method, any value can be taken as assumed mean whether it is there in the data or not but it should be centrally located in the data so that to simply the big figures in the data in order to ascertain mean of the given data through easy calculations. For grouped data, the formula for assumed mean is A+ sfd/sf where A is the assumed mean, sfd is the summation of frequency multiplied with X-A for all figures and sf is the summation of frequency or the number of element in the given data.