The problem asks to complete a table showing the frequency of family history of mood disorder by age group among bipolar subjects. The age groups are "Early" (onset defined to be 18 years) and "Later" (onset > 18 years). The categories of family history of mood disorder are: Negative (A), Bipolar Disorder (B), Unipolar (C), and Bipolar and Bipolar (D). The table also includes the total number of subjects for each family history category. Some values are missing, and we must find those values.

1. Problem Description

The problem asks to complete a table showing the frequency of family history of mood disorder by age group among bipolar subjects. The age groups are "Early" (onset defined to be 18 years) and "Later" (onset > 18 years). The categories of family history of mood disorder are: Negative (A), Bipolar Disorder (B), Unipolar (C), and Bipolar and Bipolar (D). The table also includes the total number of subjects for each family history category. Some values are missing, and we must find those values.

2. Solution Steps

Let's represent the missing values as follows:

- Early onset for Bipolar Disorder (B): $x$

- Later onset for Negative (A): $y$

- Early onset for Unipolar (C): $z$

- Later onset for the Total: $w$

From the table, we can derive the following equations:

1. For Negative (A): $28 + y = 63$

2. For Bipolar Disorder (B): $x + 0 = 57$

3. For Unipolar (C): $z + 38 = 85$

4. For the sum of Early onset cases: $28 + x + z + 53 = 141$

5. For the sum of all cases: $63 + 57 + 85 + 113 = 318$ (this equation confirms the total number of subjects)

Solving for $y$ in equation 1:

$y = 63 - 28 = 35$

Solving for $x$ in equation 2:

$x = 57 - 0 = 57$

Solving for $z$ in equation 3:

$z = 85 - 38 = 47$

The table is now complete.

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) | 57 | 0 | 57 |

| Unipolar (C) | 47 | 38 | 85 |

| Bipolar and Bipolar (D) | 53 | 44 | 97 |

| Total | 185 | 117 | 302 |

Negative (A): 28, 35, 63

Bipolar Disorder (B): 57, 0, 57

Unipolar (C): 47, 38, 85

Bipolar and Bipolar (D): 53, 44, 97

The totals of columns are 185, 117,

3

0

2. The total shown for cases is 113, which suggests that Bipolar and Bipolar (D) category should be 97 to align sum =

3

1

8. $63 + 57 + 85 + D = 318$

$D = 318 - 63 - 57 - 85 = 113$. But 53+44=97 (not 113). There is an issue with the Total.

Let's assume there is a typo in the last row of the first column, and its total is 85 (not 113).

Then for Bipolar and Bipolar (D) 53+44 = 97 and now:

Completed Table:

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

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

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

| Bipolar Disorder (B) | 0 | 0 | 57 |

| Unipolar (C) | 19 | 38 | 57 |

| Bipolar and Bipolar (D) | 53 | 44 | 85 |

| Total | 141 | 117 | 318 |

From the table, we have:

$28+y = 63$ => $y = 35$

$x+0 =57$ => $x = 57$

$z + 38 = 85$ => $z = 47$

$53+44= total D$ => $total D = 97$

The correct value to complete this table is.

$28 + y = 63$ -> $y=35$

$x = 63-28$ = $57$ - >$x = 57$

$z+38 = 85$ -> $z = 47$

Final Answer is:

$28+57+47+53 = 185 = 141$ Something wrong, with second table row or with the last total

The final completed table will have those missing values:

Later(Negative A):35

Early(Bipolar B):0

Early(Unipolar C):0

The total cases are 63,57,57,85 -> this total is wrong 318 is wrong. total would be

2

6

2.

The Completed table.

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

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

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

| Bipolar Disorder (B) | 57 | 0 | 57 |

| Unipolar (C) | 47 | 38 | 85 |

| Bipolar and Bipolar (D) | 53 | 44 | 97 |

| Total | 185 | 117 | 302 |