Statistics Test - 12

Therefore, the number of workers having a wage range (in Rs.) 110 – 120 is 45.

The abscissa of the point of intersection of the less than type and of the more than type ogives of a grouped data gives its Median. Since the point of intersection of the more than type ogive and less than type ogive gives the median on the x-axis.

An ogive is used to determine how many data values lie above or below a particular value in a data set. In other words it is used to determine the Median of a grouped data

To represent ‘the less than type’ graphically, we plot the upper limits on the x-axis.

e.g marks obtained by students are represented in grouped data as (0 - 10) , (10 - 20),  (20 - 30) , (30 - 40) .........

only upper limits such as 10, 20, 30, 40 ....... are taken for the x-axis

The lower limit for every class is the smallest value in that class on the other hand the upper limit for every class is the greatest value in that class.

To represent ‘the more than type’ graphically, we plot the lower limits on the x-axis and cumulative frequency on the y-axis to find the median.

If the less than ogive and the more than ogive intersect at (32, 48), then the median of the data is 32. Because on the graph, the point of x−axis, where less than ogive and more than ogive intersect, is the median. Therefore, the Median of the data is 32.

The most common measures of central tendency are mean , median and mode.

Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance.

Hence standard deviation is not a measure of central tendency.

The empirical relationship between the three measures of central tendencies is

3 Median = Mode + 2 Mean

The relationship is as per observation.

a distribution in which the values of mean, median and mode coincide (i.e. mean = median = mode) is called symmetrical distribution. conversely when the values of mean, median, mode are not equal, the distribution is called asymmetrical or skewed. 

knowing any two values, the third can be computed by this formula

3 median = 2 mean + mode

2 mean = 3 median - mode

mean = 1/2 {3 median - mode}

Since, Mean – Mode + Mean + 2 Mode = 3 Median
⇒ Mean – Mode = 3 Median – Mean – 2 Mode
= 3 Median – Mean – 2 (3 Median – 2 Mean)
= 3 Median – Mean – 6 Median + 4 Mean
= 3 Mean – 3 Median
= 3 (Mean – Median)