krit.club logo

Connecting the Dots... - Data Detective

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Data is a collection of numbers gathered to give some information. The first step in data handling is the collection and organization of data using tally marks.

•

The Arithmetic Mean (or simply Mean) is the average of a given set of numbers. It is calculated by dividing the sum of all observations by the total number of observations.

•

The Range of a data set is the difference between the highest and the lowest observation, given by Range=Maximum Value−Minimum Value\text{Range} = \text{Maximum Value} - \text{Minimum Value}.

•

The Mode of a set of observations is the observation that occurs most often.

•

The Median refers to the value which lies in the middle of the data (when arranged in an ascending or descending order) with half of the observations above it and the other half below it.

•

A Bar Graph is a representation of numbers using bars of uniform width, where the lengths of the bars represent the frequency or values. Double Bar Graphs are used to compare two sets of data simultaneously.

•

Probability is the measure of the chance of an event happening. It is expressed as a fraction ranging from 00 to 11. An event that is certain to happen has a probability of 11, and an impossible event has a probability of 00.

📐Formulae

Arithmetic Mean=Sum of all observationsNumber of observations\text{Arithmetic Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}}

Range=Highest Observation−Lowest Observation\text{Range} = \text{Highest Observation} - \text{Lowest Observation}

Probability of an Event P(E)=Number of outcomes favorable to the eventTotal number of possible outcomes\text{Probability of an Event } P(E) = \frac{\text{Number of outcomes favorable to the event}}{\text{Total number of possible outcomes}}

Median (for odd n)=(n+12)th observation\text{Median (for odd } n \text{)} = \left( \frac{n + 1}{2} \right)^{\text{th}} \text{ observation}

💡Examples

Problem 1:

The ages in years of 1010 teachers in a school are: 32,41,28,54,35,26,23,33,38,4032, 41, 28, 54, 35, 26, 23, 33, 38, 40. Find the range and the mean age of the teachers.

Solution:

First, we arrange the ages in ascending order: 23,26,28,32,33,35,38,40,41,5423, 26, 28, 32, 33, 35, 38, 40, 41, 54.

  1. Highest age = 5454, Lowest age = 2323. Range=54−23=31 years\text{Range} = 54 - 23 = 31 \text{ years}
  2. Sum of ages: 23+26+28+32+33+35+38+40+41+54350\begin{array}{r} 23 + 26 + 28 + 32 + 33 \\ + 35 + 38 + 40 + 41 + 54 \\ \hline 350 \end{array} Mean=35010=35 years\text{Mean} = \frac{350}{10} = 35 \text{ years}

Explanation:

The range is the difference between the maximum and minimum values. The mean is the total sum divided by the count of teachers (n=10n=10).

Problem 2:

Find the mode and median of the following data: 13,16,12,14,19,12,14,13,1413, 16, 12, 14, 19, 12, 14, 13, 14.

Solution:

Arrange the data in ascending order: 12,12,13,13,14,14,14,16,1912, 12, 13, 13, 14, 14, 14, 16, 19.

  1. Mode: The value 1414 occurs 33 times, which is the highest frequency. Mode=14\text{Mode} = 14
  2. Median: There are n=9n = 9 observations (odd). Median=(9+12)th term=5th term\text{Median} = \left( \frac{9 + 1}{2} \right)^{\text{th}} \text{ term} = 5^{\text{th}} \text{ term} Counting the 5th5^{\text{th}} term in the sorted list: 12,12,13,13,14,14,14,16,1912, 12, 13, 13, \mathbf{14}, 14, 14, 16, 19. Median=14\text{Median} = 14

Explanation:

The mode is the most frequent number. Since 99 is odd, the median is exactly the middle term of the ordered data set.

Problem 3:

A coin is flipped and a die is tossed. What is the probability of getting a 'Head' on the coin and the probability of rolling a 66 on the die?

Solution:

  1. For the coin: Possible outcomes are {H,T}\{H, T\}. Total outcomes = 22. Favorable outcome = {H}\{H\}. P(Head)=12P(\text{Head}) = \frac{1}{2}
  2. For the die: Possible outcomes are {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}. Total outcomes = 66. Favorable outcome = {6}\{6\}. P(6)=16P(6) = \frac{1}{6}

Explanation:

Probability is the ratio of the number of ways the specific event can occur to the total number of equally likely outcomes.