(A) Given $n = 20$,$\text{mean} = 10$,and $\text{variance} = 4$. $\frac{\sum x_i}{20} = 10 \implies \sum x_i = 200$. $\frac{\sum x_i^2}{20} - (10)^2 =

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(A) Given $n = 20$,$\text{mean} = 10$,and $\text{variance} = 4$. $\frac{\sum x_i}{20} = 10 \implies \sum x_i = 200$. $\frac{\sum x_i^2}{20} - (10)^2 = 4 \implies \frac{\sum x_i^2}{20} = 104 \implies \sum x_i^2 = 2080$. Correct sum of observations $= 200 - 9 + 11 = 202$. Correct mean $= \frac{202}{20} = 10.1$. Correct sum of squares $= 2080 - 9^2 + 11^2 = 2080 - 81 + 121 = 2120$. Correct variance $= \frac{\sum x_i^2}{n} - (\text{mean})^2 = \frac{2120}{20} - (10.1)^2$. $= 106 - 102.01 = 3.99$.

Class 11 Mathematics Statistics Word problem -Statistics

Difficult

The mean and variance of $20$ observations are found to be $10$ and $4,$ respectively. On rechecking,it was found that an observation $9$ was incorrect and the correct observation was $11$. Then the correct variance is

JEE MAIN 2020 All JEE MAIN

A
$3.99$
B
$3.98$
C
$4.02$
D
$4.01$

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Consider the following statements:
$(1)$ Mode can be computed from a histogram.
$(2)$ Median is not independent of change of scale.
$(3)$ Variance is independent of change of origin and scale.
Which of these is/are correct?

MediumAIEEE 2004

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The mean of $5$ observations is $4.4$ and the variance is $8.24$. If three of the five observations are $1, 2,$ and $6$,then the values of the other two observations are:

EasyMHT CET 2022

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Find the range of the given numbers: $10, 8, 12, 11, 14, 9, 6$.

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$A$ pie chart is to be drawn for representing the following data. The value of the central angle for food and clothing would be...$^o$

Items of expenditure Number of families

$Education$ $150$

$Food and clothing$ $400$

$House rent$ $40$

$Electricity$ $250$

$Miscellaneous$ $160$

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Let the median and the mean deviation about the median of $7$ observations $170, 125, 230, 190, 210, a, b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is:

DifficultJEE MAIN 2024

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Items of expenditure	Number of families
$Education$	$150$
$Food and clothing$	$400$
$House rent$	$40$
$Electricity$	$250$
$Miscellaneous$	$160$

The mean and variance of $20$ observations are found to be $10$ and $4,$ respectively. On rechecking,it was found that an observation $9$ was incorrect and the correct observation was $11$. Then the correct variance is

Similar Questions

Consider the following statements:$(1)$ Mode can be computed from a histogram.$(2)$ Median is not independent of change of scale.$(3)$ Variance is independent of change of origin and scale.Which of these is/are correct?

The mean of $5$ observations is $4.4$ and the variance is $8.24$. If three of the five observations are $1, 2,$ and $6$,then the values of the other two observations are:

Find the range of the given numbers: $10, 8, 12, 11, 14, 9, 6$.

$A$ pie chart is to be drawn for representing the following data. The value of the central angle for food and clothing would be...$^o$ Items of expenditure Number of families $Education$ $150$ $Food and clothing$ $400$ $House rent$ $40$ $Electricity$ $250$ $Miscellaneous$ $160$

Let the median and the mean deviation about the median of $7$ observations $170, 125, 230, 190, 210, a, b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is:

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Consider the following statements:
$(1)$ Mode can be computed from a histogram.
$(2)$ Median is not independent of change of scale.
$(3)$ Variance is independent of change of origin and scale.
Which of these is/are correct?

$A$ pie chart is to be drawn for representing the following data. The value of the central angle for food and clothing would be...$^o$

Items of expenditure Number of families

$Education$ $150$

$Food and clothing$ $400$

$House rent$ $40$

$Electricity$ $250$

$Miscellaneous$ $160$