Median of Discrete Series

Q.

The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers, (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers.

$\begin{array}{ccccccc}\text{Daily Income (in Rs)}& \text{10 - 14}& 15-19& 20-24& 25-29& 30-34& 35-39\\ \text{Number of Workers}& 5& 10& 15& 20& 10& 5\end{array}$

Q.

Give the formula of calculating median in frequency distribution.

Q.

Find the median of the following data distribution.

$\begin{array}{ccccccccc}\text{Marks obtained}& 20& 29& 28& 33& 42& 38& 43& 25\\ \text{Number of students}& 6& 28& 24& 15& 2& 4& 1& 20\end{array}$

1. 28.5

2. 29

3. 30

4. 40

Q.

The time (in seconds) taken by 150 athelets to run a 110 m hurdle race are tabulated below.

$\begin{array}{ccccccc}Class& 13.8-14& 14-14.2& 14.2-14.4& 14.4-14.6& 14.6-14.8& 14.8-15\\ Frequency& 2& 4& 5& 71& 48& 20\end{array}$

The numberof atheletes who completed the race in less than 14.6 s is

1. 71

2. 82

3. 11

4. 130

Q. In the given frequency distribution, which is the median term?

$\begin{array}{cc}Ageinyears& No.ofpeople\\ 15& 3\\ 16& 8\\ 17& 10\\ 18& 10\\ 19& 5\\ 20& 4\end{array}$

1. ${20}^{th},{21}^{st}$
2. ${21}^{st}$
3. ${20}^{th}$
4. ${19}^{th},{20}^{th}$

Q. Find the values of p, q, r and s in the given cumulative frequency distribution.
$\begin{array}{ccc}x& Frequency& Cumulativefrequency\\ 10& 3& p=----\\ 15& 10& q=----\\ 20& 25& r=----\\ 25& 7& s=----\\ 30& 5& 50\end{array}$

1. p = 0, q = 10, r = 35, s = 42
2. p = 3, q = 13, r = 28, s = 35
3. p = 3, q = 13, r = 35, s = 42
4. p = 3, q = 13, r = 38, s = 45

Q. The scores in an exam along with their corresponding frequencies are tabulated below.

$$\begin{array}{cc}Score& Frequency\\ 5& 3\\ 7& 5\\ 2& 4\\ 9& 2\\ 6& 4\\ 3& 3\end{array}$$
Find the median score.

1. 5
2. 7
3. 3
4. 6

Q. Find the median term of the following cumulative frequency distribution:
$\begin{array}{ccc}x& frequency& Cumulativefrequency\\ 22& 1& 1\\ 34& 2& 3\\ 39& 2& 5\\ 45& 8& 13\\ 54& 8& 21\\ 56& 9& 30\\ 68& 4& 34\\ 78& 4& 38\\ 84& 2& 40\end{array}$

1. 55
2. 49.5
3. 53.5
4. 54