STATISTICS - True/False

Statistics is a branch of mathematics that deals with the collection, organisation, analysis and interpretation of data.

In Class X, statistics deals only with ungrouped (raw) data and does not consider grouped data.

A frequency distribution table shows each observation together with the number of times it occurs.

For continuous grouped data, class intervals in a frequency distribution must not overlap.

The sum of the frequencies in a grouped frequency distribution is equal to the total number of observations.

The mean of a set of observations is always one of the given observations.

For grouped data, the mean can be calculated using the assumed mean method to simplify calculations.

In a grouped frequency distribution, the mean is computed using the mid-point of each class interval.

The median of a data set is the arithmetic average of all observations.

For ungrouped data, if the number of observations is odd, the median is the \(\frac{n+1}{2}\)th observation in the ordered list.

For grouped data, the median always coincides with the mid-point of the median class.

To find the median of grouped data, the class whose cumulative frequency is just greater than \(\frac{n}{2}\) is taken as the median class.

The mode of a data set is the value that occurs most frequently.

In a grouped frequency distribution, the modal class is the class interval with the smallest class width.

For grouped data, the mode can be estimated using a formula involving the frequencies of the modal class and its neighbouring classes.

A data set can have more than one mode.

In the context of this chapter, cumulative frequency is obtained by successively adding frequencies down the table.

A “less than” cumulative frequency curve (ogive) is drawn by plotting upper class boundaries against their corresponding cumulative frequencies.

The point of intersection of “less than” and “more than” ogives gives a graphical estimate of the mean.

In many real-life distributions treated in this chapter, mean, median and mode need not have the same value.

For grouped data in Class X, the relationship \(\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\) may be used under certain conditions.

When data are given in grouped form, the exact original observations can be uniquely recovered from the frequency distribution table.

In a frequency distribution, if all observations have the same value, then mean, median and mode are equal.

While drawing a histogram for continuous data, the area of each rectangle is proportional to the frequency of the corresponding class.

For grouped data with equal class intervals, choosing different origins (assumed means) changes the actual value of the mean.