Median
Median: Overview
This topic describes the concept of median with examples. The median is the value that separates the higher half from the lower half of a data sample. It could be the middle value for a data set.
Important Questions on Median
The following observations have been arranged in ascending order. If the median of the data is find the value of :
In a test given to a group of students, the marks (out of ) scored by them are :
Find the mean and median of the data.
The weights (in kg) of students are as follows : . Find the median. If the Weight 47 kg is replaced by 49 kg and 30 kg by 28 kg, find the new median.
John and Michel are playing a game where they shoot balloons. The rules of the games are:
- Each person can shoot two balloons one by one. The first balloon should be the one in the middle.
- The second balloon is the one at the extreme left or at the extreme right. If John is shooting, it should be the one at the extreme left and if it is Michel, it should be one at the extreme right.
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John starts the game. The game continues till one balloon remains. (Assume none of their shots are missed.)
The number corresponding to the last remaining balloon is _____.
Two friends were talking about their scores in a recent unit test.
Jim: “The scores of half the students of our class are below my score."
Tom: “But half the students in your class have a score higher than yours."
The score of Jim’s classmates, including his score, are given below. Identify Jim’s score.
Jim’s score is _____.
Shown below are the market prices of land in two cities. The numbers of plots surveyed (across the suburbs in both cities) are the same.
| Cost (Rs) / Sq ft | 3000 | 3500 | 4000 | 4500 | 6000 | 9000 | 15000 | 20000 | 30000 |
| City A | 43 | 45 | 48 | 3 | 3 | 2 | 2 | 16 | 47 |
| City B | 33 | 28 | 20 | 12 | 8 | 30 | 28 | 29 | 21 |
A middle class family is considering cities A and B in order to purchase a plot of land for constructing a home.
Which city is cheaper in terms of the cost of land?
While culturing blood, the bacteria in the blood are allowed to grow under optimum conditions for a certain amount of time and their populations are noted at regular intervals.
Shown below is a report of a blood culture performed in a lab.
| Bacterial population noted in | every 20 minutes (0.4 hour) |
| Period of observation | 4 hours |
| Total population at the end of 4 hours | 1023 |
| The time interval corresponding to the median bacterial population |
3.6 hours - 4.0 hours |
Which of the following graphs best illustrates the bacterial growth?
The sand consists of particles of various sizes as shown in the picture below.
The table shows the approximate composition (by the grain size) of the sand.
The workers at a construction site want to filter 50% of the sand (by size), which yields approximately $ \frac{1}{4}$th the weight of the sand.
The appropriate the size of the sieve to be used is _____mm.
A school is training its grade 9 students for competitive examinations. It was decided to select half of the student population of grade 9 based on their score in the screening test.
Their scores in the screening tests are shown below.
The cutoff score is _____.
The ages in years of 12 students participating in an inter-house competition in school are:
9, 7, 11, 13, 9, 16, 11, 18, 15, 15.5, 8, 10
They take part in Under 10, Under 12, Under 14, Under 16 and Under 19 categories. On Sports Day, the students less than 9 years were replaced by students in the under 19 year old category.
Due to this, the central representation of the team shifted from the under 12 years age group to under
_____ years category.Find the median of 15, 17, 13, 19, 20, 12, 16, 14, 18, 22.
While solving the above given question during her exams, Andrea by mistake reversed one of the numbers and got the median as 17. The number from the set which Andrea changed is _____.
(Note: Assume that Andrea knew how to find the median correctly.)
The age of people on the ration card of a household is given below. If the middle most value of Daniel’ family is 44 years, then the value of x is_____.
28, 32, 36, x + 1, x + 3, 48, 50, 52.
The number of children in families are as follows, find their median :
| No. of children | |||||||
| No. of families |
Find the median of the observations . If another observation is added to the above data, what would be the new median?
Find the mean, median and mode for the following test scores of students.
The following are the heights of students in a class.
and .
If the median height is , then find the value of .
