Measures of Central Tendency
Class 11 · Economics
4 ideas in Class 11 Economics, explained in plain words, with games and quizzes to practise.
Arithmetic Mean
Part of: Mean and Median
Mean divides totals by counts; assumed-mean shortcuts shift work; weighted means weight importance; combined means pool groups proportionally.
Why it matters. Means summarise fast. Weights reflect importance.
Formulas
- Mean = sum of observations / number of observations.
- Assumed-mean method: mean = A + (sum of d) / N with d = X - A.
- Step-deviation method: divide deviations by a common factor, then multiply back.
- Weighted mean = sum of (weight x value) / sum of weights.
Key words
- Arithmetic mean
- : The sum of all observations divided by their count.
- Assumed mean
- : A guessed centre A from which deviations are measured to simplify work.
- Step deviation
- : The shortcut dividing all deviations by a common factor first.
- Weighted mean
- : An average weighting each item by its importance share.
- Sum of observations
- : The total of values used as the numerator of the mean.
Try it in two minutes
- Total the values.
- Divide by count.
- Weight when needed.
Try at home. Mean your test scores.
Median for All Series
Part of: Mean and Median
Odd counts pick centre; even average pair; discrete cumulates to half-total; continuous interpolates inside median class; ogives read graphically.
Why it matters. Medians resist outliers. Classes need interpolation.
Formulas
- Position of median = (N + 1) / 2 th item in an ordered array.
- Discrete median = size of the (N + 1) / 2 th item.
- Even count: median averages the two middle values.
- Continuous median class holds the N / 2 th item, not the (N + 1) / 2 th.
- Median = L + ((N / 2 - cf) / f) x h.
Key words
- Median
- : The middle value splitting ordered data into two equal halves.
- Median position
- : The rank locating the median as the (N + 1) / 2 th item.
- Cumulative frequency
- : Adding frequencies upward to find where the middle item falls.
- Median class
- : The class holding the N / 2 th item in continuous data.
- Ogive reading
- : Reading the median value off a cumulative frequency graph.
Try it in two minutes
- Sort or cumulate.
- Find middle rank.
- Interpolate in class.
Try at home. Median house rents nearby.
Mode by Inspection and Grouping
Part of: Mode and Choice
Mode repeats most; inspection spots clear winners; grouping tables untangle ties; modal class interpolates with neighbour gaps.
Why it matters. Popular values guide stock. Groups need formulas.
Formulas
- Mode = L + (D1 / (D1 + D2)) x h.
- D1 and D2 use frequency differences ignoring signs.
- Mode needs equal class intervals and an exclusive series.
Key words
- Mode
- : The value occurring most often in a data set.
- Inspection
- : Picking the clearly most frequent value by eye.
- Grouping table
- : The table untangling tied frequencies to reveal the modal class.
- Modal class
- : The class with the largest frequency in continuous data.
Try it in two minutes
- Count repeats.
- Group if tied.
- Interpolate modal class.
Try at home. Modal shoe size at home.
Choosing the Average
Part of: Mode and Choice
Mean suits symmetric totals; median splits skewed incomes; mode stocks popular sizes; geometric means rate growth; quartiles split quarters.
Why it matters. Wrong averages mislead. Purpose picks the tool.
Formulas
- Mean suits symmetric totals; median splits skewed incomes; mode stocks popular sizes.
- Q1 has 25 percent below it, Q3 has 75 percent below it, and Q2 is the median.
Key words
- Mean use case
- : The average fitting symmetric data where extremes matter.
- Median use case
- : The average fitting skewed incomes and open-ended series.
- Mode use case
- : The average fitting popular sizes and qualitative data.
- Quartiles
- : The cut points dividing ordered data into four equal shares.
Try it in two minutes
- Check the skew.
- Name the purpose.
- Pick the average.
Try at home. Pick average for rents.
What your child will practise
- Arithmetic Mean: Desert Puzzle (Clue Puzzle)
- Arithmetic Mean: Desert Quick Fire (Quick Fire)
- Choosing the Average: Space Puzzle (Clue Puzzle)
- Median for All Series: Candy Quest (Flip and Match)
- Mode by Inspection and Grouping: Jungle Quick Fire (Quick Fire)
- Quiz: Arithmetic Mean (8 questions)
- Quiz: Choosing the Average (8 questions)
- Quiz: Median for All Series (8 questions)
- Quiz: Mode by Inspection and Grouping (8 questions)