The problem provides a partially completed table showing the frequency of family history of mood disorders by age group among bipolar subjects. We need to complete the table and draw three different types of bar charts (multiple, component, and percentage bar charts) based on the completed table.

1. Problem Description

The problem provides a partially completed table showing the frequency of family history of mood disorders by age group among bipolar subjects. We need to complete the table and draw three different types of bar charts (multiple, component, and percentage bar charts) based on the completed table.

2. Solution Steps

First, we need to complete the table. We can use the given totals and individual cell values to find the missing values.

* Row 1 (Negative (A)):

Later (L) = Total - Early (E) = $63 - 28 = 35$

* Row 2 (Bipolar Disorder (B)):

Early (E) = Total - Later (L) = $57 - 38 = 19$

* Row 3 (Unipolar (C)):

Early (E) = Total - Later (L) = $85 - 44 = 41$

* Row 4 (Unipolar and bipolar (D)):

Later (L) = Total - Early (E) = $113 - 53 = 60$

* Column 2 (Early (E) = 18): We already have all these values

* Column 3 (Later (L) > 18):

Total = Sum of individual disorders = $35 + 38 + 44 + 60 = 177$

Now we have the completed table:

| Family History of Mood Disorder | Early (E) = 18 | Later (L) > 18 | Total |

|---|---|---|---|

| Negative (A) | 28 | 35 | 63 |

| Bipolar Disorder (B) | 19 | 38 | 57 |

| Unipolar (C) | 41 | 44 | 85 |

| Unipolar and bipolar (D) | 53 | 60 | 113 |

| Total | 141 | 177 | 318 |

The second part of the question asks us to draw the following:

*Multiple Bar Chart: this chart type displays bars of different colors side-by-side for Early and Late onset for each disorder. The y-axis would represent frequency, and the x-axis would represent the type of family history of mood disorder.

*Component Bar Chart: This chart type represents bars stacked to show totals for each type of family history, with different colors representing Early versus Late onset. The y-axis would represent the total frequency and the x-axis represents the type of family history of mood disorder.

*Percentage Bar Chart: Similar to the component bar chart, but representing data as percentages. Each bar will represent the total for a specific family history of mood disorder. The total bar height will be 100%, and segments of the bars will represent the percentages of Early versus Late onset. To calculate percentages, we use: $Percentage = (Value / Total) * 100$.

Negative (A): Early = $(28/63)*100 \approx 44.4\%$, Later = $(35/63)*100 \approx 55.6\%$

Bipolar Disorder (B): Early = $(19/57)*100 \approx 33.3\%$, Later = $(38/57)*100 \approx 66.7\%$

Unipolar (C): Early = $(41/85)*100 \approx 48.2\%$, Later = $(44/85)*100 \approx 51.8\%$

Unipolar and Bipolar (D): Early = $(53/113)*100 \approx 46.9\%$, Later = $(60/113)*100 \approx 53.1\%$

3. Final Answer

Completed Table:

| Family History of Mood Disorder | Early (E) = 18 | Later (L) > 18 | Total |

|---|---|---|---|

| Negative (A) | 28 | 35 | 63 |

| Bipolar Disorder (B) | 19 | 38 | 57 |

| Unipolar (C) | 41 | 44 | 85 |

| Unipolar and bipolar (D) | 53 | 60 | 113 |

| Total | 141 | 177 | 318 |

(Description of bar charts given in the solution).