Solutions

1.The difference between the maximum and minimum observations in the data is

Range

Mode=`l+(f_1-f_0)/(2f_1-f_0-f_2) times h`

=`2+(7-5)/(2times7-5-3) times 2`=2+`4/6`=2+0.67=2.67

n=79 ⇒ `n/2=79/2=39.5`, c.f=26, f=24, l=`(20+19)/2=19.5`,h=10

Median=`l+(n/2-cf)/f times h`

=`19.5+(39.5-26)/24 times 10`=`19.5+135/24`=19.5+5.625=25.125

3-5

Modal class=40-50

Upper boundary of modal class=50

Median class=40-50 ( because `n/2`=14)

lower boundary of median class= 40

sum of boundaries =40 +50 =90

Mode=`l+(f_1-f_0)/(2f_1-f_0-f_2) times h`

Here `l=4, h= 2, f_0=5,f_1=7,f_2=3`

∴ mode=`4+(7-5)/(14-8) times 2`

=`4+4/6`=4+0.66=4.66

`n/2=31/2=15.5`

it is in class 34 so median is 34

`n/2=100/2=50`

Median=`l+(n/2-cf)/f times h`

=`69.5+(50-41)/35 times 5`=`69.5+9/7`=69.5+1.28=70.78

answer:4

answer:1

The mean of first n natural numbers is 15, then the value of n is

sum of first n natural numbers = `(n(n+1))/2`

mean of first n natural numbers=`(n(n+1))/2n=(n+1)/2 =15`

n = 30-1=29

If the median of 10 observations 20,22,27,28,32, x+2,39,40,41,50 arranged in the ascending order is 34, then the value of x is

Median= average of middle terms

`(32+x+2)/2`=34

x=68-34=34

A car manufacturing company announced that most of the people are showing interest to purchase red colour cars. The measure central tendency they selected for this observation is

Mode

The Mean of 100 observations is 49. By an error 60,70,80, are registered as 40,20,50 respectively. The correct mean is

60+70+80=210

40+20+50=110

210-110=100

so mean is 49+`100/100`=50

In a graphical representation of a frequency distribution, if the distance between mode and mean is k times the distance between median and mean, then the value of K is

Formula:Mode=3median-2mean

Given: mode-mean=k(median-mean)

∴ 3median-2mean-mean=k(median-mean)

3(median-mean)=k(median-mean)

∴ k=3

Mode of 1,2,3,8,10,11,16 is

No mode for this data

The arithmetic mean of a+3d, a+d, a-d and a-3d is

Mean= `(a+3d + a+d + a-d + a-3d)/4`

= `4a/4`=a

Which of the following is not a measure of central tendency

Range

6,2,9,11,3,4,9,7,13,1 from this data which statement is true?

arranging the data in ascending order 1,2,3,4,6,7,9,9,11,13

Mean=`65/10`=6.5

Mode = 9

Median = `(6+7)/2=13/2=6.5`

So,Mean = Median < Mode

A survey is conducted for popular TV show which central tendency used for this

Mode

A is defined as A={ n ϵ N /(1+n²) < 10) then find the Mean of elements in A

A={2,5}

Mean= `(2+5)/2=7/2=3.5`

In a grouped data Class size h, Mean A.M, assumed mean A and the mean deviation is d then the relation between these 4 is

A.M= hd+A

The Graph used for the Median is

Ogive curve

The Mean of first ‘n’ Natural numbers is

`((n(n+1))/2)/n=(n+1)/2`

2,4,6,7,4,2,8,11,4,8,12,4 find Mean- Mode for this data

Mode=4

Mean= `72/12=6`

Mean-Mode=6-4=2

8,14,16,21, x, y,28,30,33,38 Median is 25 and y-x = 2 for this data then find x and y

Median=`(x+y)/2`=25

y+x=50

y-x=2

2y=52 ⇒ y=26

x=50-26=24

For a data sum of observations is 576 and the mean is 18. Then find number of observations in this data

Number of observations=`576/18=32`

Mean for a+1, a+3, a+4 and a+8 is

Mean= `(a+1+a+3+a+4+a+8)/4`

`=(4a+16)/4`=a+4

In a data 13 observations arranged in ascending order then median observation of this data is

7^th observation

Cumulative frequency used for measure

Median

Average of 12,15,13,20,25 is

Average=`85/5=17`

In a data All observations are added by 5 then the mean of new data will be------ to previous data

added by 5

Median of 24,20,32,18,28,16,25 is

Arranging the observations in ascending order

16,18,20,24,25,28,32

Median is 24

Mode of 9,8,7,7,6,3,7,2,1,7,9 is

7 (maximum frequency)

Mode of a data is

3median- 2mean

Range of first five numbers is

5-1=4

Ogive curve is a

Cumulative frequency curve

Mid value for the class x-y is

(x+y)/2

Intersecting point of less than ogive and more than ogive is (42,18) then the median is

42 ( x co-ordinate)

The mode of the data 3, 4, 5, x is 5, then x is

5

Mean of first four odd prime numbers is

Mean=`(3+5+7+11)/4=26/4=6.5`

Required values for more than ogive curve is

More than cumulative frequency, lower boundaries

Class size of 11-20 is

10

Median and mode of a data is 73.9 and 76.7 then mean is

2Mean= 3median-mode

2mean= `3times 73.9-76.7`

mean=`(221.7-76.7)/2`=72.5

If l=40, F=25, f=24, C= 20, n= 70 then median is

`n/2=70/2=35`

Median=`l+(n/2-F)/f times C`

=`40+(35-25)/24 times 20`=`40+200/24`=40+8.33=48.33

Mode of first ‘n’ Natural numbers is

No mode

Mean of 9, 11, 13, k,18,19 is k then k is

k=`(70+k)/6` ⇒ 6k=70+k

5k=70 ⇒ k=14

Which measure is used for elect a leader

Mode

How many modes possible for a data

It may possible one mode, two modes or manymodes. some data has no mode also

50,42, a, 21,19,12 median is 25.5 then find a

Arranging the data in ascending order 12,19,21,42,50,a

Median is 25.5.So, a is more than 21 and less than 42

Re arranging the data we get 12,19,21,a,42,50

So, `(21+a)/2`=25.5

21+a=51 ⇒ a=51-21=30