Solutions of Unit 6 Basic Statistics

Solutions of Unit 6 Basic Statistics of Class 10 math will help students understand following concepts:

1. Grouped Frequency Table:

• Constructing Grouped Frequency Table: Organizing raw data into a table that groups values into intervals (class intervals) with their corresponding frequencies.

2. Histograms:

• Constructing Histograms:
  • With Equal Class Intervals: A bar graph where each bar represents the frequency of data within equal intervals.
  • With Unequal Class Intervals: Similar to the above but adapted for intervals of different sizes.

3. Frequency Polygon:

• Constructing a Frequency Polygon: A line graph that shows the frequencies of the different intervals by connecting the midpoints of the tops of the bars in a histogram.

4.Cumulative Frequency Table:

• Constructing a Cumulative Frequency Table: A table showing the cumulative totals of frequencies as you move through the intervals.

5.Cumulative Frequency Polygon:

• Drawing a Cumulative Frequency Polygon: A graphical representation of cumulative frequency using a line graph.

6.Measures of Central Tendency:

• Arithmetic Mean:
  • By Definition: The sum of all data values divided by the number of values.
  • Using Deviations from Assumed Mean: Calculating the mean by assuming a value as the mean and adjusting for deviations.
• Median: The middle value when data is arranged in ascending or descending order.
• Mode: The most frequently occurring value in a data set.
• Geometric Mean: The nth root of the product of n values, used for data sets involving rates or ratios.
• Harmonic Mean: The reciprocal of the arithmetic mean of the reciprocals of the data values, useful in calculating averages of rates.

7.Properties of Arithmetic Mean:

• Recognizing Properties: Understanding the characteristics of the arithmetic mean, such as sensitivity to outliers.

8.Weighted Mean and Moving Averages:

• Weighted Mean: The mean where each value has a weight reflecting its importance.
• Moving Averages: Calculating averages over specific intervals in time-series data to smooth out fluctuations.

9.Graphical Estimation:

• Estimating Median, Quartiles, and Mode Graphically: Using graphs like ogives and histograms to estimate these measures.

10.Measures of Dispersion:

• Range: The difference between the highest and lowest values in the data set.
• Variance: The average of the squared deviations from the mean, representing data spread.
• Standard Deviation: The square root of the variance, showing the typical distance of data points from the mean.
  Formulas of all these topics are listed here

This Solutions of Unit 6 Basic Statistics equips students with essential tools for analyzing and interpreting data, which is crucial for various fields such as economics, business, and science. Here is a You tube link for this units 6 basic statistics video lectures. Interested in trigonometry? we are heading there starting from Unit 7 solutions.