Measures of Cen...

A football player scored the following number of goals in the $$10$$ matches:
$$1, 3, 2, 5, 8, 6, 1, 4, 7, 9$$
Since the number of matches is $$10$$ (an even number), therefore, the median
$$=\dfrac{5^{th} \text{observation} +6^{th} \text{observation}}{2}$$
$$=\dfrac{8+6}{2}=7$$
Is it the correct answer and why?

If the mean of variate X in distribution 2.6, then the value of k is

The points scored by a basket ball team in a series of matches are as follows:
$$17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28$$
Find the median and mode for the data.

A total of $$25$$ patients admitted to a hospital are tested for levels of blood sugar $$(mg/dl)$$ and the results obtained were as follows:
$$87$$ $$71$$ $$83$$ $$67$$ $$85$$
$$77$$ $$69$$ $$76$$ $$65$$ $$85$$
$$85$$ $$54$$ $$70$$ $$68$$ $$80$$
$$73$$ $$78$$ $$68$$ $$85$$ $$73$$
$$81$$ $$78$$ $$81$$ $$77$$ $$75$$
Find mean, median and mode $$(mg/dl)$$ of the above data.

The mean marks (out of $$100$$) of boys and girls in an examination are $$70$$ and $$73$$, respectively. If the mean marks of all the students in that examination is $$71$$, find the ratio of the number of boys to the number of girls.

Mean of $$50$$ observations was found to be $$80.4$$. But later on, it was discovered that $$96$$ was misread as$$ 69$$ at one place. Find the correct mean.

The median of the data
$$78, 56, 22, 34, 45, 54, 39, 68, 54, 84$$ is

The mean of $$25$$ observations is $$36$$. Out of these observations if the mean of first $$13$$ observations is $$32$$ and that of the last $$13$$ observations is $$40$$, the $$13$$th observation is :

If the mean of the observations:
$$x, x + 3, x + 5, x + 7, x + 10$$ is $$9$$, the mean of the last three observations is

The mean of $$100$$ observations is $$50$$. If one of the observations which was $$50$$ is replaced by$$ 150$$, the resulting mean will be :