A left skewed histogram is a histogram that attains a peak (which is the mode) towards the right side of the graph and has a “tail” towards the left side.

This means that the data has contains a greater number of larger values compared to smaller values.

The above image is an example of a left skewed histogram. We can see that it has a “peak” towards the right with its mode lying somewhere between 70 and 80.

The graph has its “tail” towards the left side. *We use the side in which the tail lies to decide whether the histogram is left skewed or right skewed.*

If a histogram is skewed towards the left, we say that the histogram has negative skewness and that the distribution is negatively skewed.

**Relationship between Mean, Median, and Mode in a Left Skewed Histogram:**

We have the following relationship between the mean, median, and mode.

Mean≤Median≤Mode.

The reason for the mean being smaller than the median and the mode is that in a left skewed distribution, there is a greater frequency of larger values which increases the median and mode of the data.

The value of skewness will always be negative for a left skewed histogram because the mean is less than the mode in a left skewed distribution.

**Real-Life Example of left-skewed data:**

The death rates of individuals compared with age is an example of left skewed data. If we were to plot the age on the X- axis and the number of deaths in that age group on the Y-axis we would get a left skewed histogram.

This is because there will be greater number of deaths among the older population. There will be relatively less frequency of deaths among the younger population.

**Construction of a left skewed histogram:**

Consider the following data showing the marks obtained by a group of students in an exam worth 100 points.

Class Intervals (Marks obtained) | Frequency (Number of students) |

0-10 | 1 |

10-20 | 1 |

20-30 | 2 |

30-40 | 4 |

40-50 | 7 |

50-60 | 14 |

60-70 | 16 |

70-80 | 22 |

80-90 | 21 |

90-100 | 15 |

We plot the above data and obtain the following histogram,

Once again, notice that the mode of the histogram lies towards the right and the tail lies towards the left.